The exploration was a step down since there weren't as many chests and crap in high ledges that you'd need to reach using Trinity. Or the complete lack of platforming that was in the original. The original's more large stages really really made for some excellent exploration. You were always teased in Kingdom Hearts. See a treasure chest! But how the fraking hell do I get to it? This game would build up each ability you earned so that you'd have a Metroid-like sense of progression for finding and exploring certain areas or things.
The battle system was about as fun, probably more so depending on who you talk to, but it was so easy. Personally, I prefer the original. The quick events in KHII are cool, but they're essentially tapping triangle. Yawn. Triangle. Still, I think that KHII's boss fights are better than the original's, but the core battle system in the original is more satisfying. In KHII I mostly mashed the attack button over and over, KH1 was totally different. I remember the first time I fought Riku's last form. Holy shit. KH1 may have been made for kids in mind, but the difficulty is up there so that I think anyone can get something from it.
I especially loved how you had to shift through menus with the d-pad. You would multi-task like a mofo in KH1 and it gave me adrenaline rushes. It was balls out AWESOME kicking butt with attack button while going through menus to pick magic or items. Especially against the tougher bosses in the arena. Whoo boy. It was something I never really felt from an action rpg, that tension. KHII lacks it.
I'm one of the few people who liked the gummi ship in the original. It was Space Harrier-lyte. I got a kick out of making a cool decked out Gummi Ship, naming it Ragnarok and owning everything in sight. I liked making a giant cock with a pair of balls that could shoot shit from its laser hole. But KH2 took this to the next level. The gummi ship system in 2 is really, the biggest evolution between the games.
The sidequests aren't as good as the ones in the original either. Remember the awesome quest list in the main town in KH1? You had to do a specific number of things and then you unlocked more crap as you went on? Is there really anything like that in KH2?
Remember when you boot up KH and you have to pick between attack power, defense, or magic power? Is there anything like that in KHII? I don't remember. It's things like that which made KH1 for me and why I have played it numerous occasions.
The story? Let's not bring up the story.
I just felt that the original KH had more rewarding battle system, sense of exploration, level design, platforming, rewards, sidequests, story, characters and really...everything, with the exception of bosses and gummi ships.
It was just a totally creative action rpg. No, the battle system wasn't the greatest and the camera would sometimes make me want to kill myself, but that game was fun as hell. KH1 stands as one of my favorite ps2 games; KHII was just an unforgettable but still fun ride.