I've played FFXI since it came out like 7(?) years ago and still do.
I even met my fiancee on there!
Anyway, I've played all three versions.
PS2: Laggy, 640x480 resolution so the menu and chatbox take up a good portion of the screen. Poor graphics. But it does the job.
XBOX360: Looks the best of all three. The graphics were updated a little for this version.
PC: Obviously the best, but not because of the graphics. With the PC version, you have access to all sorts of plugins and hacking tools (good (like mini-maps) and bad (like teleporting around)). You can edit the interface, colors, even change the models of whatever you want.
Not only that, but you can change the resolution of the onscreen elements so make the chat box and menus smaller.
The best thing is get the PC version, then see if you can get a used copy of the 360 version since once you make the account on the PC, you can access on any version.
Little trivia for you, the reason that there are some limitations in the game, such as limits on the amount of items you can carry, is because of the PS2. The PS2's memory is limited and can't handle as much as a PC or 360 would, however, you can't really give the advantage to some consoles and not the other. It wouldn't be fair.
PS: Go to Valefor. That's my server!