FXAA is no Real Anti Aliasing, all it does is putting a Filter over your "Rendering Screen" and therefore in some Way is a "Free Cheap AA".
In Short : It only costs you like 0,1% Performance.
What costs Performance are Parallax Occlusion Mapping (It's ugly in FFXIV... Low Res Textures FTW), and SSAO (HBAO / HBAO+ are extremely GPU Intensive)
Shadows doesn't even come close to the amount of Power you need compared to SSAO or Parallax.
Turning Parallax off and putting SSAO to Low-Mid-High will give you a better Framerate then simply turning off FXAA (Tho I would turn this off aswell, it simply blurs)