Marvel Heroic RP (aka Cortex Plus Fantasy Heroic) is my favorite Supers rpg. It could certainly do JLA - handling widely varying power-levels is one of the systems signatures.
I find fate is pretty good for handling supers... Venture City has a pretty nice set of aids for using fate to run super games, not sure if there are others but the base game handles it so well you may not need to look for modules...