Personally, KH2 is my favorite game of the series. In the game play aspect of it anyway. I think BBS has the best story (I haven't played Coded or 3D).
KH2's combat system seemed more fluid and was fun. The only bad thing about it was it was always fast paced combat with all of flashy moves. KH1 did have it right in that aspect where you could go from slow to fast paced. The Drive Forms, Reaction Commands, and Limits all add to this fast paced action.
The Gummi Ship is a lot more fun and enjoyable because it is more fast paced.
Jiminy's Journal was badly set up in KH2, but its something that I can overlook and I honestly got used to.
The ability to skip scenes was a good addition.
Lastly, I actually like how crazy and I think I saw someone say convoluted the story got after this game. It gave something to talk about. We knew from all the stuff that was left out that there would be answers and sequels. It made the game much more interesting. I've heard of a few people say KH1 was confusing, I understood everything that happened in that game (except the secret ending until I played KH2 obviously). Nothing was a mystery except the secret ending (Roxas and Riku and The World That Never Was), what was gonna happen to Riku and Mickey (they went to Castle Oblivion after escaping the Realm of Darkness), and what did the note Pluto have at the end of the game say (I don't think that was ever answered actually)? Also, where would the road that Sora and Co. lead which we found out was Castle Oblivion. Everything else in KH1 was explained in game. KH2 left it up to speculation until later which I liked. I mean, we might not have some of the threads on this site if it wasn't for the story of KH2.
KH2 definitely deserves this.