Street Fighter III is not yet supported in MAME (if it ever will be)
Basically, it is too new
From my understanding it is also notoriously difficult to emulate due to the self-destructing ROMs and encryption. Although I've heard the CPS2Shock team have managed to decode some/most/all of the encryption, but are holding off due to the game's relatively recent age.
But as mentioned, it's not like the old days of SNES where if you wanted an arcade perfect SF2 it was a ROM, Jamma board, or nothing. In this day and age, console ports are just as good as real arcade machines. XBox, Playstation2 and DreamCast all have competant versions of SF3. I have Third Strike on DreamCast, and it's excellent. Somebody pointed out that there are a few timing differences in some of the high-end infinite combos, but I'm honestly nowhere near good enough to notice minor differences like that.

What about the Alpha and Zero series? eh? 
They were all CPS2 except for "SFA3: Upper" which was Naomi.
The entire Alpha/Zero series (and a bazillion clones) all work fine in MAME, Kawaks, RAINE, and many others.