I'm a big fan of the FE, and ended up buying an FM3a for the additional *minor* features that the Nikon design team incorporated to the original FE/FM to make an excellent product even better. Minor things like Dx code reading (don't often use it), brighter viewfinder, straight-pull camera back opening, and the film cartridge window. Also the promise that if the battery fails, I can still run the shutter.
Functionally they are exactly the same. I use the FM3a regularly now and the FE is in reserve. But honestly, I didn't really need to upgrade.
Even more honestly, I've been using my old Olympus OM-1 that I've had forever more often lately than the Nikons. I think the Zuiko 50 f/1.2 is great for color and the Nikkor 50 f/1.8 is great for B&W...but of course that's just my opinion.