I have read both series, and I prefer Harry Potter by far. I feel that Twilight is a good read, but it is not good literature. I also feel that Twilight has made standards for men impossible. Not only is Edward Cullen intelligent, handsome, multilingual, well-read, plays and writes music, physically strong, a gentleman, a rogue, doting, and has a great family, he can also grant eternal youth. I mean...is this what women are looking for? This is not human. It is a fantasy, and I'm really concerned about what Twilight may be doing to young minds.
Furthermore, I like that Harry Potter is political. It has so many more complex and thoughtful themes than Twilight. The whole thing with Hermione and the House Elves speaks volumes about civil rights. Additionally, the whole thing with The Quibbler being sort of a "tabloid" type newspaper, where no one pays attention to it at all and calls it crazy (and they read the mainstream newspaper, I forgot what it's called), but then when Voldemort takes over, everyone starts reading The Quibbler...calling it much more trustworthy. I find this really interesting. This reminds me of Alex Jones. I don't endorse all (or even most) of the guy's ideas, but he has been right about a lot of things...vaccines, raw milk, he predicted that Rick Perry would run for president (months before it happened) when Rick Perry promised he wasn't going to run, and he predicted the defaults in Europe. Same thing with Gerald Celente. I didn't really catch on to the Quibbler analogy until lately, when I started getting really upset with how the mainstream media has been treating Ron Paul, and started finding out why.
In any event, I don't know that I would call Harry Potter good literature, exactly, but I feel that it's a more relevant work, and that it is better written. But, as I said, I also really enjoyed Twilight. It was a page-turner, I'll give it that.