I don't have an XBox nor a PS2. From what I understand in order of "correctness" (ie: sound/graphics/etc) it goes:
1) Dreamcast
2) XBox
3) PS2
XBox also has "XBox Live" for online play, which is popular amoungst tournament players (check out the shoryuken.com forums, or ozhadou.net for Aussie players). Third parties have told me the graphics are best on Dreamcast. PS2 graphics are supposedly "fuzzier" (lower res perhaps?). Not my words (again, I don't own one and can't comment nor confirm such statements).
"Arcade perfect" in my eyes would be everything right down to the "insert coin". Console versions will always be different, and sometimes for the better (ie: new tournament/versus modes, online play, extra characters/music/etc). All modern consoles are CD/DVD based, so you're always going to get load times.
At any rate, you have to decide whether or not the cost of a CPSIII unit (complete with suicide batteries and the rest of their dramas) is worth your money for a single title compared to a $20 dreamcast and a second-hand copy of the game bought off ebay for a few more bucks. Remembering also that DreamCasts can output straight to 15-pin DSUB (with appropriate cable) for superb picture quality on real arcade monitors. No hardware mods needed (asides for maybe a controller hack if you want to play on sticks).
For me as a casual player, the DreamCast version was a winner.
