I did not like Eccleston in the beginning but I began to appreciate that hidden somberness in his character, the idea of him carrying the weight of what he has seen. Same thing happened when Tennant started... wasn't quite sure what to make of him. I watched most of the episodes first because I missed the Christmas Invasion. Once I saw the first Christmas Invasion and again saw that same somber attitude, he was OK to stay. :P
Tennant brings back those quirky behaviors that were best in Tom Baker and Sylvester McCoy. I hope he sticks around since there aren't that many regenerations left...
Oh and don't read this Spoiler:
MY FAVORITE SCENE HAPPENS IN SEASON THREE!!! YOU SEE THE TARDIS FLYING OVER ROADS OF LONDON CHASING AFTER A CAR!!!! AAAAAHHHHHHHHHHH!!!!!!!! Yeah I geeked out over that one.
I still want to know what happened with Paul McGann as the Doctor! I really liked the character he brought as the Doctor in that one time movie on Fox.