The main difference I felt between the two franchises was that MoH was more run-and-gun arcade style action with a WW2 twist, where as CoD was a little more tactical.
The main thing with me is I've played a lot of FPS games since a very young age, so I look for things that change the genre, MoH only brought a new perspective on things, but CoD changed the way it was done. I do have to admit though I did like MoH:AA, especially the D-Day landing level, but nothing beyond that, it felt too much like a classic FPS game, shoot the enemies before they can shoot you.
I preferred CoD for it's reliance on co-operating with your squad, if you ran ahead into enemy lines, you died fast, if you took point and covered for your advancing squad as well, you'd have an effective way of taking down your enemy.
I'm not bashing MoH here, I'm just saying the franchise doesn't appeal to me, I prefer CoD overall. I like the concept of MoH:Airborne, but it's not the game for me. :)