Graphics: this is a major step up from the previous games. The worlds are much much bigger and better looking than the previous games.
More impressive to me though is that the art style works so much better. KH2 felt a bit more jarring with the real life worlds. This game does it so much better.
Music: for whatever reason I feel like the music is less present in this game than the previous ones.
The first two games were so wonderful starting up the menu with this song. And this game just hasn't reached that for me.
Overall story: it feels a little lacking. A lot of the story just seems to be revolving around what players like me missed or forgotten and it feels a bit strange. It just gives a strange tone.
World stories: a step up from KH2, a step down from KH1.
The stories are a lot like KH2 in that they are more like retreads of the same story from the movie, with a few exceptions. But it's done better here. In the second game there were instances where they put in famous lines of dialogue from the movie and it was fine very poorly. They were just thrown in without context and the dialogue didn't even make sense.
I still feel it's a step down from KH1.
Gameplay:
This game introduces so many more mechanics than the previous games. Some of them are great, some arent. On the whole I feel good about this game. But for a while it was really putting me off of the game.
Conclusion:
On the whole, in some ways it's probably the best KH game, some ways it's probably the worst. Overall though I still prefer the first two games. But I can understand why someone might find this to be their favorite.