I have the same problem my friend

i7 3630qm
16gb DDR3
7970m running 13.8 Beta 2 which is supposed to increase FPS in FF XIV

I can run it on maximum but with the same results as you. At least if the desktop variation of my card is having the same issues I can def blame it on optimization :P , unfortunately were going to have to wait for eithe AMD or Square to finish optimizing it properly

My desktop 6950 gets the same results as well haha.....oh well. For now I run it on Laptop and Desktop high and it seems fluid and smooth and vysnc capped at 60 so I will just leave it there for now but it is aggravating because I know it can go higher without any problems. My GPU's are not even 100% when running the game