My favorite book is definitely Eclipse. As other people have said in this topic, you get to see more of the development of Edward and Bella's relationship, but there are also a lot of other reasons. You also get more of the other characters. You learn both Jasper and Rosalie's stories and learn how they came to where they are in the Cullen family. Twilight was amazing, but all you really got in that story was the development of Bella and Edward and vampires in general, and New Moon was more about Jacob and the wolves, but in Eclipse you get more character development from the rest of the Cullens. But I think my favorite aspect of Eclipse is the struggle in it. With both Jacob and Edward there and fighting for Bella, you get a much better mix of emotions from all sides. Twilight was all about love, New Moon was more about pain, but in Eclipse you get love in forms of romantic love, friendship, family, you get pain in more ways than just loss, there's inner torment. Also, another part that I forgot to mention was the fact that you get to actually witness a real battle. The fight with Victoria at the end of the book is the closest we come to a real vampire fight which is one the parts I was really looking forward to when I started to read the series.
Plus, Eclipse has my all time favorite scene, in the tent, the conversation between Edward and Jacob. I just absolutely love that part!
"You held out your hand, and I took it without stopping to make sense of what I was doing. For the first time in almost a century, I felt hope." ~ Jasper Hale