I recently acquired an FM2n to accompany my battered (but much loved) FE.
They are physically identical on the outside, and as stated just the light meter marks them apart in general use.
That said, the analogue needle style meter on the FE is just more enjoyable to use. The FE does have a very dark viewfinder though, in low light it can be hard to read the light meter.
The FM3 is the dogs licky-bits IMHO. More costly, but it combines all the best elements of all that era of Nikon cameras. The mechanical independence from a battery for shutter speed, the lovely analogue light meter, the compact body (the F3 just feels a bit uncomfortable in my hands by comparison).
I paid more than I really had to for a near mint condition FM2n from an eBuyer with a good track record (worth the extra cost for a camera in such beautiful condition).
I would say though (slightly contradicting myself) I seem to nail exposures better with the FM to the FE. It may just be that the camera is in better condition and more accurate, but I find myself trusting my gut more when it's borderline whether to go up or down a stop. The centre-weighted light meter, makes a quick compare and contrast of the exposure levels in a scene nice and simple and I feel I can average it out better with the FM.