Well, the story in MM is largely throwaway. You can ignore it if you wish and just concentrate on the maps, whereas in AW the story is a lot more obtrusive.
I always preferred MM over AW due to the hex-based design and Zone of Control. Those two things alone make a big difference in gameplay.
Has anyone here ever played the game OGRE? It's an hex-based wargame that was converted into a computer game. I loved playing that on my Atari 800, and when MM came out it reminded me a lot of OGRE. In OGRE, the forces were lopsided (one player controlled a huge battletank, the other side had a bunch of much weaker units), but the futuristic setting and hex-based design were kind of like MM.