Funny how this topic comes back around every now and again.
The Dreamcast version of Sonic Adventure is, by basically all accounts, the definitive way to play the game... unless you mod the PC version. As of late, there's been the popular Dreamcast Conversion mod for SADX PC which is being done to restore everything about the Dreamcast's graphics, effects and quality. Even small details like the bubbles which flow on Chaos 0, 2, and 4 were recently restored.
You can see basically all of the downgrades done to the DX release here
. They are numerous, and quite frankly, you just shouldn't bother with the PC release unless you... don't have a Dreamcast. And even then, you could probably just emulate it and still get a better experience.
As for SA2, the Battle release is honestly fine. There are some changes to sound mixing that are more pronounced on the Gamecube release, but it's perfectly acceptable, plus you get much more multiplayer content in the Battle release. The modern release for 360, PS3 and PC is identical, but sound mixing is actually far worse compared to the originals. I believe mods exist to fix that though. Combined with a netplay client, and honestly, SA2B for PC could be considered the definitive release otherwise. It's also way cheaper compared to picking up a proper copy of SA2 for Dreamcast.