I'm not sure what the connection was, but I had the same issue (Windows 7 64-bit, no stuttering in any other game) and tried just about everything until I read somewhere that this fixed it for someone else: I had the VMWare program VirtualBox installed. I simply uninstalled it. Fixed; no more stuttering in FFXI.

Weirdest fix ever but it worked for me -- I hope you have VirtualBox installed >.>