The graphics are noticeably worse than on Dreamcast, mostly in cutscenes, like Amy's pink teeth. I don't remember exactly, but I want to say that audio quality and audio balance are also worse on Gamecube or something like that, which is not good because the audio is already not great on Dreamcast.
It's not nearly as big of a difference as Adventure 1, but the Dreamcast version is still better. People will argue for the Gamecube version, but the only things they have to use in their argument are the expansions to the Chao Garden and multiplayer.
Dreamcast also has the rad VGA box for glorious pristine video while getting better than composite or maybe S-video out of a Gamecube is an expensive pain and potentially impossible if you have the wrong Gamecube, so there's also that, even though that's not really anything to do with the game itself. I mean I guess you can just use a Wii if you really wanted to, but then you wouldn't be playing the Dreamcast version anyway. This game has really damn nice graphics for a 2001 console game on hardware released in 1998, too, so you might as well enjoy those graphics; the game still looks pretty great today!
This is partially due to the lighting. The developers couldn't get the lighting systems of Sonic Adventure 1 and 2, both of which were very advanced lighting systems for console games of that era, to work properly on Gamecube. I don't know the reason for this, but the lighting in particular is way worse on the Gamecube versions of both games.
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