I read the first of the Harry Potter novels, directed at roughly the same age group but I didn't care for them. The Twilight books were a little better written (though, as with all teen novels, written with the tendency to hit you over the head repeatedly with any important plot point but that's to be expected). I enjoyed the character development of the side characters at least as much as I enjoyed the main characters...possibly a fair bit more.
I found Harry Potter vastly superior. The overall story was just so much better. Twilight focuses on character interaction... and by character interaction, it's pretty much Bella and Edward to the exclusion of almost everyone else. Bella's human friends literally become "Oh, now he's dating her" later on. That's all. You get back story with the vampires, but you hardly ever go into detail like the main couple.
After 4 books, I was SO over it.
The only part of the series I liked, literary-wise, was near the beginning of the second book, when it just lists the months and otherwise blank pages. I thought it made the point simply and directly; probably because the rest of the **** book was Bella crying over Edward, in great detail. It was a neat deviation, but it says a lot (to me, anyway) when the best part of the series in writing is where you write practically nothing.
As for the series itself, well, the 4th book was my favorite just because something actually HAPPENS in it. But as said, the long-awaited *** scene was totally glossed over. Another example of fail (I understand the target audience, but there are so many sexual allusions made already that some vague but hot description would have been perfect there).
I definitely don't hate it due its popularity. It's just, unlike series like HP, I just cannot understand how people think the writing is good. It might be the frame of mind you're in, though. I enjoy HP, but I'm sure a lot of Twilighters think it's not that good and would rather have several chapters describing Edward's abs as some kind of marble statue. Can you imagine having *** with that? Ugh.