To be honest, a lot of ideas in Harry Potter were taken from mythology or other authors. The same can be said about Twilight, but at least Meyer changed it up a bit with her sparkly vegetarian vampires. Of course, any sort of world involving dragons or werewolves will borrow from preestablished myths, but neither storyline stands too much above the other in this respect. You can't argue that one has more originality than the other.
Both storylines feature dark plots and themes, some of which may be subtler in Harry Potter, but certainly present nonetheless. In Twilight: fear, isolation, mortality, the presence of evil, etc. In Harry Potter: death, the presence of evil, oppression, etc. Rowling actually said the major theme of her books was death. Both stories are perhaps intended for more mature audiences. Twilight may appear a little 'darker' or 'more mature' because at the start, it involved teenagers, while Harry Potter involved children. Children are seen as innocent, while teenagers might be seen as a lot less innocent. Both are different stories with different characters, and should be considered as such.
I can't give a solid answer to either of them, they're about equal in quality to my eyes.
