From my experience using MLAA in Total War: Shogun 2 and Deus Ex: Human Revolution, post processing AA is definitely better than no AA at all. It's not as good as MSAA and has some blurring drawbacks, but IMO the blur isn't nearly bad enough to outweigh getting rid of those jaggies at a fraction of the cost of MSAA. This is especially true of game engines that use deferred rendering, which includes BF3. Forcing MLAA through the driver controls is also better than forcing MSAA in the drivers for games that don't have native AA support (ie Mass Effect), especially since AMD has been putting performance improvements into the tech.
Regarding Battlefield 3 specifically, I can't give my opinion because I don't have the game. But I thought the post AA in BF3 was MLAA? AMD has been pushing MLAA on PCs while FXAA is Nvidia's post AA tech, and BF3 is an AMD sponsored game. Shogun 2 and Human Revolution were AMD sponsored games and they used MLAA (HR also had an FXAA option, though MLAA was supposed to be the best option).
(As an aside, I find it amusing that on consoles the 360 often uses FXAA while the PS3 uses MLAA [albeit CPU based], opposite of the designers of the GPUs in the consoles)
Edit: here's some image comparison done by HardOCP. First, a screenshot of no AA, 2x MSAA, and 4x MSAA:
Now no AA and the FXAA settings:
And 4x MSAA directly compared to FXAA High:
To me, the FXAA does cause some blur but at least it gets rid of the jaggies. MSAA doesn't seem to do much of anything at all...