Game Versions

There exist several versions of the game:

Arcade Neogeo MVS
Neo-Geo AES Home Console
Playstation 2
Xbox 360 - Xbox Live Arcade
Dreamcast (Titled Fatal Fury: MOTW in the US)

Version Differences

Most Neo-Geo emulators support a Prototype version of Garou:MOTW that should be avoided at all costs. This version has many bugs and changes from the released versions that make unsuitable for real play.
The Neo-Geo AES (home console) and Neo-Geo MVS (arcade) versions are considered the only pure versions, and they are identical. Support for Garou is available on all worthwhile Neo-Geo emulators.
The Japanese Playstation 2 and Xbox 360 versions are the best home console versions. The controls are very tight and the game play is perfect. On the PS2 version during play the words 'Guard Cancel' do not flash on the screen like the other versions do. On the 360 version it fixes that problem. The training mode for PS2/360 are superior to all other versions, they allow for recording and playback of the training dummy's actions. So for practicing setups and other single player training, the PS2/360 versions are the best, even better than the pure Neo-Geo versions. Another thing to take notice is that both the PS2 and 360 versions run at a faster framerate than the original arcade MVS/AES versions. Only takes a bit to adjust to the speed difference and shouldn't cause any problems when running tournaments. The online play over Xbox Live is better than previous SNK releases, but is still bad nonetheless. GGPO/Supercade/Arclive are your better options for online play. The PS2 version also contains the arranged soundtrack, while the 360 version does not (as it is based directly on the original Arcade version).
The Dreamcast version is the worst of all possible versions. It offers nothing over the Neo-Geo versions other than the unlockable image gallery and the arranged soundtrack mode. Inputs are delayed, Terry's stage lags the game and some versions show problems with sound effects delaying as much as 2 seconds from when they should play. Some of Terry's voice samples are also not the ones from the game, but from as early as Real Bout Fatal Fury Special. If possible, select the original soundtrack option instead of the arranged soundtrack, and play on the original GD-ROM to lessen these effects. Even with these adjustments, this is the worst option for play; even playing on an emulator will be more satisfying.