I've been having the same problem in both FFXI and FFXIV since I switched to a GTX660ti.

Initially I thought it was a bad card but after numerous burn ins and using different software, playing movies, reading the forums and in general having no other issues with the card I can only conclude it's a driver issue, quite possibly caused by the new Kepler architecture.

I have a gtx550 and it runs both games just fine the 550 also uses the Fermi Architecture, which when it was first released also had issues with FF, the only thing we can do is continue to submit complaints to Nvidia and SE in hopes it moves our problem moves up on their priority list and they address the issue sooner rather than later by amending the driver software.

Until then my xiv will continue to look terrible on my gtx550 and my xi will continue to run on it too...