I like Adventure 2 overall better. I do like that the levels are spread out better for characters. There's 4 different playstyles to have(kart racing being the 4th), and they're rather polished. Tails' stages are a bit subpar compared to Eggman's, unfortunately, but not bad by any means. Worst part is the Get 100 Rings emblems...
My favorite are the hunting stages in general, but the radar got nerfed from Adventure 1. Otherwise, it was perfect. Not all the stages were, of course. Security Hall, Meteor Herd, and Mad Space needs some work. The first two are just a pain at points(lolrandommeteor taking away all your rings, and the time limit is very annoying) and the third one isn't nearly as bad, just really huge and can be hard to find stuff at a decent speed.
Shadow's levels felt a bit lacking at times compared to Sonic's, but that's mostly because the 3 clone characters(Shadow, Tails, Rouge) were made later in development, so most likely their stages weren't nearly as planned out. I do like White Forest and Radical Highway, but the other two were fairly cheap to go through with overuse of enemy placement/pitfalls. It's why the racing stages aren't really high on my list of preferences for the games.
That said, the Chao system was massively improved. No longer did you need special fruits to make them Dark or Hero Chao. You can pet them without it not registering(the hell? That should've been fixed in the original gamecube port...). You don't have a character who cannot swim, so it's far easier to rescue them from what looks like drowning. The various mini-games are easier to train them for due to the Chaos Drive system.
I still enjoy Adventure 1 overall(I do wish Big's fishing was more polished), but as noted, it's flawed. The courses aren't particularly great at times(Sonic's final stage can let you die if you jump just a little too high...), although I don't remember exactly why it does that.