KH1 focuses too much on the novelty of Disney meets Square in terms of plot. By the end of the game, something interesting does developed and that s what the rest of the series is more focused on. The actual original plot is pretty interesting if a bit convulated and sounds pretty silly on paper, once you get past that, it gets better. BBS just has the fortunate help of not needing all the baggage from other games to explain things, though it unfortunately raises more questions about the overall universe.
Gameplay has also improved with a better camera that makes platforming not seem like a chore and combat gets new tweaks and mechanics in each installment. In BBS case, your characters equip skills that can be toggled in a shortcut menu a la Crisis Core, but using certain skills in succession has a chance of making a character enter into special fighting modes. So using a lot of Fire magic or skills can make your character into a mode where they gain automatic fire elemental traits for their attacks and special combos and moves. Even in these modes, building long combos and using other skills/spells can unlock second and finally third tier combat modes that are ridiculously awesome to use and watch. So combat has some interesting flow that goes with it, and setting up your skills has more importance than just their basic function.
The game also offers three different characters to play as and all three actually do play differently. Ventus is speed, Terra is power, and Aqua is magic and they all get exclusive fighting modes, skills, spells, and Shotlocks. There is definetly more variety in combat and its actually pretty fun. As I said its the best gameplay in the series so far. If you're still hesitant, at least rent it and give all three characters a whirl.