Personally, I'd pick HP. I’ve read both of the series, by the way. Twilight fans, don’t even bother reading this. It’s obviously too long for your puny little damaged brains.
1-Characters. There are hundreds of characters in the HP series. The ones that we are all familiar with can easily be compared to a real person, and each develops during the years.  They each have differing personalities and physical characteristics, and are very realistic. And unlike the Twilight characters, they also have flaws and quirks, which make them much more believable than the Twilight guys. Take Neville Longbottom, for example. When we first meet him, he’s a bumbling, nervous, clumsy little kid who can’t seem to do anything right. After a while, he then develops into this strong, steady character who’s previous and serious lack of self-confidence has disappeared, making way for the courage, daring, talent and wit that he seemed to nervous to release in the early years. Now the characters themselves:
Bella: If she’s supposed to be so plain, why does she have so many admirers the minute she comes to Forks? Bella Swan literally means beautiful swan; swans supposed to be graceful and delicate, and she‘s supposed to be plain.. Her only seeming ‘flaw’ is that she’s clumsy. She has a weak personality and very poor character development. She is a complete damsel in distress, incapable of handling herself without her charming Edward. She devotes herself to him and cannot live without him, giving us the message that women cannot function without a man, which is total bullshit. As my current T-shirt says “A woman without a man is like a fish without a bicycle.” Bellatrix Lestrange could totally kick her ass.
Edward: Meyer’s biggest mistake. He is the very definition of ‘perfect’. He’s charming, ‘beautiful’, and everything a girl could dream of in a guy. Unfortunately, this makes in incredibly unrealistic. There is no such thing as a truly ‘perfect’ person, but Meyer seems to be telling us that they are the only people to fall in love with. If you believe her, you are going to be left alone. There are plenty of flawed and yet wonderful people in the world. In my opinion, Edward’s only flaw is that he has no flaws. I find it very hard to find ways to make him believable, and not purely a fantasy. Let’s talk ‘vampires’, now. And are they even vampires? No. Meyer completely ignores the traditional definitions and characteristics of vampires. Yes, hers such blood, but not human blood. They cannot go out into the sun, but only because they look really pretty and sparkle. They are perfect, but, even for a fictional people, they are unbelievable. Where are the stakes? Where are the shadows, the coffins, garlic, evil, mystery and danger? These creatures are not vampires. The only similarity between them and their namesake is blood-drinking.
Jacob: Someone who could have been a good character, until Meyer ruined him. He had a definite personality, a few flaws, and good development. Until Meyer decided to complete him. Now he’s completely devoted to Bella, and suddenly he falls in love with a year-old child. Although having different characters is good, Meyer implies that this is completely normal and is a good thing. Grown men being romantically interested in children. That’s not good; that is wrong, disturbing, and an unhealthy idea. And the werewolf thing? Werewolves are not supposed to be able to transform whenever they like. It’s supposed to be a curse, not a gift.
HP time!
Harry: The main character of the books. The big protagonist, and a wonderful creation. And though I myself am not a particular fan of his, his actual character is remarkably well made. He develops an incredible amount throughout the books, from a nervous little kid who just found out he was a wizard, to a confident young man with great talent and skill. Physically, he’s like everyone else; flawed, nothing particularly remarkable except for a scar that is, most of the time, hidden. He is nowhere near perfect, and so the reader can identify themselves with his character. His personality is just as normal; he is stubborn, courageous, intelligent, and has a variety of emotions.
Hermione: Though smart throughout the entire series, there is more to her than just incredible brain power. Capable of taking care of herself, she differs greatly from Bella. Her personality, along with the rest of the HP characters, extends beyond her love interests. It takes her a long time for her and Ron to really be able to realize and acknowledge their feelings for each other, even going so far as to pick friendship and loyalty over love. She is strong, stable, and an almost complete opposite of Bella Swan.
Ron: Bumbling, the one kind of left out and thought of last, he is still a remarkable character. Though strong, determined, and loyal, he is also moody and can let things get between him and his friends. He is probably the most believable and realistic of the characters, for though he cares about Harry and Hermione, he can get jealous and emotional, although he values their friendship and forgives them and himself.
Dumbledore: Does Twilight have and really cool guys with beards? No. Dumbledore and Snape are probably the most interesting characters, the ones who have a lot more behind them than the others, things that have both affected them and motivated them to their current positions. Dumbledore is strong, powerful, caring, understanding, eccentric, and wise, and though he seems like the one who will always survive, the one who always be around and almost completely flawless, he is much deeper than he appears(which is pretty deep in the first place.) Beneath the continuously calm, collected strength-radiating exterior we learn is sadness, doubt, and a darker, flawed past. Rowling teaches us, with Dumbledore, that even heroes bleed, and that the best of us are destined to die. In her books, it’s not just the bad guys that are lost. Such is life.
Snape: Probably the most difficult and complex character, besides Dumbledore himself, Snape proves to be incredibly more than we would have thought. At first nothing more than a background character, we learn that Snape plays a very large part in the series and how the course of events came to be. Seeming incapable of love and tenderness, it comes as a complete surprise when it is revealed than he was, and still is, in love with the main character’s mother. His past and his motivation becomes incredibly twisted and complex, and though he is the one to really cause Voldemort to go after Harry, and so making the entire series, he is also the one who is working behind the scenes, fixing something here and there to ensure that evil does not triumph. Although we’re not really sure what side he’s on for almost the entire series, the cruel, cold, and sarcastic Snape turns out to be one of the best. Cold, collected, he is not a particularly likeable character, from his appearance to his personality, and though some may not like him, he is almost the direct definition of an anti-hero.
Ginny: I decided to throw her in here to point out the differences between her and Bella, the two being the love interests of the main guys. She is strong, sturdy, and can take very good care of herself, much unlike Bella. She does not curl up into a ball and go into clinical depression when Harry tells her that he cannot be with her, she goes on and continues with her life. She is not all emotional and fussy. She does not have admirers the minute she gets into school; in fact, she is constantly teased and it’s only until her fifth year that she ever seems to get any romantic attention. She outshines out expectations of her, and develops from a scared little girl into a confident and strong woman.  
One more thing that I’ve noticed: Meyer does not have a wide variety of people. There are no eccentric personalities, nobody who could be described as crazy or dotty (like Luna). There are no strong females, no homosexual people, and barely any gingers. Absolutely no diversity. Where are the redheads? JKR has the entire Weasley family! Meyer? Victoria and Edward. That is just sad.

2-Plot. Though both can be called interesting, I’d have to admit that the HP stories are far more interesting when it comes to what happens in the books. Harry and his friends must battle their way, physically and mentally, through increasingly difficult obstacles as they try find ways to defeat the Dark wizard who is taking over the magical world, and as Harry develops, so do the books, from a simple writing style to one that requires concentration and understanding, from a book with an easy-going nature to a complex and detailed style of writing.  Twilight: a human girl and a vampire fall in love, even though their relationship is difficult and dangerous. Twilight is a romance(and a cheesy one at that); HP is adventure, romance, mystery, and everything under the sun. Every chapter there are twisting and interesting little things, and things from the first chapter or even the first book that seem completely unimportant are re-introduced later as having great significance. There are little things here and there that, when you notice them, always give you a little jolt or shiver. For example, the Marauder’s names are listed as Moony, Wormtail, Padfoot, and Prongs on their map. You soon find that they died in the exact reverse order of how they were listed. There are twists left and right that will often leave you speechless. “But it wasn’t Snape. It wasn’t even Voldemort….It was Quirrell.” Who would have expected? After Snape threatening the stuttering guy, Snape supposedly jinxing Harry’s broom, Snape showing up with a bite from Fluffy, and it was Quirrell? That was one of the ‘Woah, holy crap!’ moments that often appear in JKR’s books. Things like Hagrid being blamed for opening the Chamber of Secrets, Sirius being innocent and Scabbers being the guilty ‘dead-man-walking’, Moody actually being a supposedly dead Death Eater, Snape(who always turned out to be the good guy) killing the good-est character, and then learning that Dumbledore and Snape planned the whole thing all along! The twists, the complexity in Twilight? Virtually nonexistent. Everything is too perfect, too happy-go-lucky. There are no problems, so bad situations, nothing turning out bad. Everything is solved, everything ends well. If people are going to base their life around Twilight and expect everything to be as Twilight portrays, they are going to be seriously disappointed.

3-Lessons. Woo-hoo, now we get to the fun and insulting part! Let’s just get to the chase.
Twilight lessons: From Bella, women are not capable of living beyond their boyfriend or husband. They are incapable of helping themselves, and must always rely on their boyfriend to be able to do things. They are helpless, weak, and always need a man. This is what I like to call bullshit. I will quote it again: “A woman without a man is like a fish without a bicycle.” An example that this is crap: After the divorce, my mother single-handedly takes care of a teenage girl, works until she can work no more, and takes care of the house and animals without a man at her side for a good ten or so years(I help her a lot, though. She’s not as young as she used to be.) I, a teenage female, have had a boyfriend for almost ten months now. We get along very well, but if he dumps me tomorrow I will not be reduced to a useless lump threatening to kill myself in depression. As another note, the marriage and kid thing? She's, what, eighteen? She says she's not the kind of girl who gets married right out of school, and what happened? She got married right after school. Then she gets knocked up. She's barely an adult. Now, some of you may believe that it's a good thing to get married and have kids right away, and that's your opinion. But me, personally, I think she shouldn't have had a kid so young. She's not responsible or mature enough.
Now, from Edward. Edward is…a very special person. He is flawless, perfect in every way, everything that a woman could dream of in a man. He is not real. He is, though it is portrayed as love and protection, is abusive, dramatic, and dangerous. If he had really cared for Bella, he would not have left her. He would have chosen the risk of hurting her other than leaving her to suffer. What is up with their relationship?  He falls in love with her because she smells good? She loves him because he is ‘perfect and beautiful’? They would kill themselves if the other gets hurt? There is a thing called ‘moving on’ and ‘getting over it’ and ‘getting on with your life’. They relationship is too dramatic, obsessed, and unhealthy. Although it’s a good thing to be willing to sacrifice what you want to let somebody else have what they want, what Edward does when he tells Jacob that Bella could have ‘puppies’ if she wanted is going way too far. What is up with their daughter, by the way? There is a difference between a natural birth and ripping open the girl’s stomach to take out the disturbing little demon child. That birth was the only fun part of the entire series; it was funny seeing Bella the Mary-Sue suffering. As another point, I have to mention; pedophilia is BAD. These are little kids we are talking about. It’s not funny, it’s not sweet, that Jacob and Quil fall in love with small children. It’s just disturbing. Going back to Edward’s lessons: It teaches you that if you cannot find the man or woman of your dreams that your life is worth nothing, and if you do, that you should completely devote yourself to them and ignore everything else. It teaches us the we should fall in love with perfect beings, as they are perfect and so are the only ones we can love. You wasn’t somebody flawless, someone who is not human. We should completely exclude ourselves from society, ignore our friends and abandon our families for a boyfriend. If you  believe that, you’re going to die alone and cold. Flaws are flaws, but it’s a good idea to have some. Lets people know that you’re human. To err is human.
Harry Potter lessons: Like Twilight, the most important lesson is that love conquers all. Unlike Twilight, though, this kind of love extends beyond obsessive passion. There is more than just making you and your love happy. HP teaches us that sometimes we have to sacrifice what we want, and even our lives, for the greater good. It teaches us to value friendship and the love that binds us all. Harry and Ginny split it because, like Edward and Bella, their relationship could be dangerous for the females. But, unlike Edward and Bella, Harry and Ginny are capable of being mature enough to accept the others decisions without completely breaking down and loosing their minds. A life without love is hardly a life worth living, but there are more kinds of love other than killing yourself in mad desire. Voldemort is unable, for a while, to touch Harry because Harry is capable of love. Voldemort, or Riddle, having never loved or felt love, is not able to understand it and so brings his downfall, with Lily’s sacrifice for her son, Snape’s love for Lily, and just the love all around. Really, Voldemort is really the only ‘bad’ character in the novel, because of his complete lack of love and understanding of it. Even bad-ass Bellatrix has love in her, and the snooty Malfoys turn their backs on Voldy in search for their son. The Harry Potter series also teaches us, unlike Twilight, that there are worse things than death. Twilight tells us that we should seek immortality, fear death and try to defeat it. HP is the opposite. There is no way to defeat death, and so no point in fearing it. There are, again worse things than dying in the world, such as living without love. Death is inescapable and imminent, for each and every one of us. We cannot run from it forever, and so must make with out lives what ever we can, by living and loving and doing as much possible good for the world as we can.
It also teaches us that even the smallest voice can make the biggest difference, that even the weakest of us can rise above the others. Pain, like death, is also inescapable. To live is to hurt, and you must accept that it is impossible for everything to go right all of the time. But to built on your strengths, you must also acknowledge your weaknesses. Learning to live with your faults can be worth more than just making yourself more powerful and trying to ignore your flaws, for if you do, they can be your downfall if you do not acknowledge that they are there. See them and learn them, and so build your defenses for them. Trust in yourself, your friends, and your enemies, but not to the extent of being cocky and over-confident. Voldemort, for example, with the belief that he is the most powerful wizard in the world, focuses on becoming more powerful and ignores his weaknesses, ultimately leading to his downfall. Lockhart is another good example of being over-confident, being good only at lying and taking other people’s triumphs for himself. You must also trust your enemies, but don’t misinterpret what I am saying. You must accept that they may be able to defeat you, but you must have courage. Cowardice will get you nowhere, and even those who have the least confidence in themselves may very well be able to roar like a lion when they need to(see Neville Longbottom). But do not trust completely, for even your friends may betray you. Also, thoug it is touched on briefly , another lesson is that killing rips the soul apart. Don’t kill. Very bad idea.
Be true to your friends. Though they may be different, though they may not be popular and though you may get upturned noses from being with them, they are still your friends, and you are their friend. Another lesson is to not abandon your family. Bella’s willing to completely abandon both her family and friends to be with Edward, but, for example, Hermione has to exclude herself from her parents in order to protect them, although she goes back to them in the end.

I’ll probably add more later. Peace.