Unfortunately, FF XIV is made from an internal engine, so they could have optimized for just Intel based PCs. So, the short answer is "yes, it might be".
For example, UE3 based engines run usually better on Intel/nVidia PCs than AMD/AMD PCs or even Intel/AMD (this one is smaller though).
Try OC'ing the 8320 and see if it makes a difference.
Well, I did try overclocking (using the Catalyst with the 13.11 beta drivers), but it made the game really unstable and was really choppy and strange when I started it up and played it. I turned off AMD overdrive and everything went back to normal.
EDIT: Just for clarity; I meant I overclocked my CPU (the 8320). I haven't tried overclocking my GPU.