For me there appears to be very little performance impact from enabling AA. I currently appear to be CPU rather than GPU limited though. R9 290X & FX-9590.
My experience.
AA off makes things just look ugly to me; but then I hate running with AA off on a 1440p monitor as well.
FXAA works but tends to make things soft or blurry.
MLAA doesn't have the blurry problem, but it's not actually doing a great job at getting rid of jaggies either. It also appears to have the most impact for my setup. Although, as I said, it's fairly small.
SMAA is as sharp as MLAA but seems to be doing a better job of getting rid of the jaggies and performance impact is minimal.