FXAA has nothing to do with AA...
They are two seporate things.
AA will smooth-out the jagged edges of pixelated polygons. EG, makes your sword-edge blend to the background, instead of just drawing the pixels on the edges ON/OFF.
FXAA is an After Effects bonus. It alters shadows, hues and colors, flame-warping, fog depths, creates motion-blur, simulates natural Depth-Of-Field blur on distant objects, simulates lighting-iris effects, Lightning-flashes across whole maps, etc...
If you have FXAA on, and AA, that is a major performance-hit. (Parts of the game use FXAA even if you turn it off, like the HUD blur, some rooms, most lights in dungeons. Auto-iris that darkens the screen when you go from a light-room to a dark-hall.)
FXAA is less demanding in most situations, as it does nothing most of the time, until it does. Mostly the effects are after the scene is rendered, as opposed to AA which renders in the scene, and is taxing as you see more traingles/edges which need softening. The illusion of AA in FXAA is due to Depth-of-field blurring, as your sword/objects are usually smoothed/blurred as they get further away, thus, no ON/OFF look to the pixels, unless you get right-up on something, near the camera, you will then see the sharp edges come back again.