The only differences are as follows:
I THINK the Gamecube version might have better framerate or something, (usually the case with GC vs PS2)
The PS2 version has a demo for X8 that you can get easily in the game, (and stays unlocked once you get it)
The GC version can be hooked up with a GBA to locate hidden tokens with the GBA screen as a radar, for an extra figure vending machine in Central Tower, which you can look at in the Sky Room trophy room. The PS2 version does not have this vending machine.
Other than that, there are no real drastic differences. Depends which you care about more. An unlockable demo of X8, (which is slightly different than the final in terms of some music tracks and some graphics, as well as difficulty) or virtual collectible figures.
Also what White-Jet said, about the CM save file thing for X8.
Although you can access the same hidden fight with a code at the title screen of X8, rendering the save file unnecessary.