There are a few things that are different:
There is a secret ending to this game, you don't have to get it in Proud mode, but its much easier in Proud mode as explained here
You also get the "Badge of Pride" for beating it on Proud.
You also unlock the even more challenging Critical Mode when you beat all other difficulties. Beside making the secret ending even easier to unlock that mode is just there to make u hate life, increasing damage of the enemies and actually decreasing yours.
No other changes are listed per difficulty level, not even on the KH wiki article made specifically to list the differences per level by game.