At least eighty percent of the plot of a Kingdom Hearts game comes from the Disney source material that was adapted in order to make the various worlds that Sora & co. visit on their road to finding their friends. So, it is vitally important that the adaptation from classic Disney movie to videogame stage is pulled off well. Unfortunately, I don't think the transformation went anywhere near as smoothly in Kingdom Hearts II as it did in the original Kingdom Hearts. Whereas Kingdom Hearts I creatively adapted the stories of the movies to better fit the gameplay and over-arching story of the game, Kingdom Hearts II usually resorted to simply re-treading the original plots of the movies (with the often glaring inclusion of Sora). As a result, I found the worlds of Kingdom Hearts II to be significantly lacking in comparison to those of the original game.
The biggest problem with a slavish retelling of the original movie's plot is that it is impossible to capture the feel of a movie within the confines of a video game. Movies and video-games are very different mediums with very different needs and different tools at their disposal. In particular, unless a developer painstakingly recreates every last detail from a movie scene in video-game cutscene form, that scene will have less impact in the game than it did in the original movie. Since it is virtually impossible to do this without resorting to expensive FMVs (or replaying clips from the original movie), trying to recreate the original emotional impact of a movie (particularly classic Disney movies loaded with nostalgia for a lot of players) is a hopeless endeavor. This problem is made worse by a particular quirk of the videogame medium: players generally don't like watching cutscenes without gameplay interspersed to break it up. Because of these factors, game developers cannot entertain players by simply bombarding them with cut-scene versions of familiar movie scenes.
Sadly, Kingdom Hearts II often did resort to just this approach. The most egregious offender is KH II's Atlantica stage, which at one point retells more than 70% of the movie's plot in thirty minutes of cut-scene broken up only by a quick chance to save and a three minute interactive cut-scene event. While not as bad, many of the other KH II worlds similarly tried to compress the plots of entire movies into hour and a half long stages (Mulan and Pirates of the Caribbean are notable examples). However, they also tried to tell most of the main plots of these movies, and relied heavily on cut-scenes in order to do so. The result is a lot of relatively short stages that feel like the cliff-notes versions of the classic movies and are too light on exploration and serious action.
In comparison, the first Kingdom Hearts generally focused on a smaller part of each individual movie, and built a semi-original plot line around that one aspect. For example, the Wonderland stage of Kingdom Hearts is built entirely around a scene from the movie where Alice is held on trial by the Queen of Hearts. Saving Alice from the wrongful allegations becomes the plot for Sora and company during their stay in Wonderland. While places from the movie become areas in the game, the game focuses on making the player feel like he is exploring Wonderland himself, instead of forcing the player to watch Alice explore Wonderland as she did in the movie. Furthermore, Kingdom Hearts introduced a change to the plot to make it fit in with the overarching plot of the game: the Queen accused Alice of trying to steal the Queen's heart (the Heartless were the real culprits, of course). A similar amount of change can be seen in the original Atlantica stage, which cut out the entire "Ariel falls in love with a human" plot to focus on Ariel's relationship with her father (once again bringing in the main game plot in a convincing manner). In these ways, the stage lets the player experience the magic of the movie in an interactive fashion, and makes the movie world feel like an integrated part of the larger Kingdom Hearts world. It also kept the action firmly focused on the players actions and the game's main characters, as it should be.
The Kingdom Hearts II stage that succeeds the best at feeling like a really fun stage is Timeless River. Since Timeless River was based on old six minute cartoon shorts, there really was no plot to speak of to base the stage on. Instead, the stage was all about playing up the mood of those old-school cartoons. Timeless River successfully transmitted that wacky and frantic mood and allowed for a lot of fun gameplay at the same time.
I should at this point mention that many of my favorite Disney adaptations from the first Kingdom Hearts did not involve Disney specific worlds at all. One of the best was introducing The Beast, the Princesses, and Maleficent into Hollow Bastion, a world designed for the game specific plot. The appearances of these characters did not rely on the plot of their original movies whatsoever; yet, their roles in the game were nonetheless interesting, and helped make Hollow Bastion an incredible stage. Another great choice from Kingdom Hearts was transforming a section from Fantasia into a boss-fight in the final dungeon. Chernobog had no plot, but the monster and its awe-inspiring music was one of the most unforgettable aspects of descent into the final dungeon.
Significant adaptation is required in order to translate a movie into a videogame. This is doubly true for large cross-over games like Kingdom Hearts. I think the original Kingdom Hearts was much more successful than its sequel at making the Disney worlds interesting by focusing on creatively adapting smaller, easier to manage pieces of the movies into something that functioned as a game first and foremost.