Because FFXI interfaces better with the PS2 version and Xbox is using the Windows version.
FFXI is an MMO. MMOs are notorious for framerate issues and for general bugginess, including random crashes for no reason. It's not a system-specific issue, it's the nature of MMOs.
The 360 version is still in active development. The 2013 expansion Seekers of Adoulin is coming out on the 360 and the PC outside Japan. It's only going to be avaliable on the PS2 inside Japan. Kinda sucks if you have FFXI on a PS2 or PS3 with PS2 BC.