There isn't much difference except build quality and price. The FM10 is a simple plastic and the FM3A is the high end manual camera that keeps the old match-needle metering method that many older photographers love. The FM3A would be my choice despite the higher price. It could last you a lifetime.
Next time you are in a shop that has an FM-10, give it a look over and compare it to some other low end SLRs such as the Olympus OM-10, Vivitar, Cosina, and others. Notice that the parts look exactly the same, and in fact, they are all the same camera with different lens mounts. Except that you are paying a bit more for the Nikon mount.
I personally would not recommend this camera, as I think that you are better off spending more money on a higher quality rig, or even spending the same money on a older, but better, used camera.
Not that an inexpensive camera has a lot to do with how good your photos will be. that's all between your ears. It's just that the more cheaply made your camera is, the more likely it will fail or break at the worst possible moment (one day into a two week vacation, your best friend's wedding, etc...).
I don't know much about the FM-3, but the old FM-2 was a really nice camera.