If you're on PC, it sounds like your framerate might just be.. low. A low framerate in FFXI as an example, would cause my character to move slower than anyone else.. This is because a large portion of how character movement was handled was by the client, not the server, so if your framerate was slow you'd be moving slower because your game is quite literally running slower. This is probably the case with FFXIV too.

If you're PS3, I have no idea. Perhaps it is overheating.