Bottom line after reading pages and pages of comments on game sites from people that played both games:
MW3 is the more pick up and play, rinse and repeat, been there done that game for the casual players and people who like to build and track stats, prestige etc.
And has the BETTER single campaign.
BF3 is the one with better visuals, and is more realistic "war" like, with more tactics and intelligence, and what sounds like more mature players and hardcores playing it.
But honestly, I just can't and haven't gotten into a FPS mulitplayer since the Unreal days. And I have a feeling it's pretty much the same formula, no matter how you dress it.
Both are GOOD in their own ways and both have pros and cons. But...it's time to move on from this debate! lol Too many other good games that deserve attention! Skyrim, Batman AC, Crysis 2, AC Revelations etc lol