This is my short review between BF3 and MW3, I will review several aspects of each Games. Remember these are opinions, so they are not hard facts. IGN Officially was in favor of BF3 more, but here is my review:

Lets start off with single player.
Singleplayer:
Battlefield 3:
BF3's single player has a fairly basic storyline, with many twists and turns, some parts were predictable, some were not, The first few missions really show off its engine, such as the Hotel. Blowing it up? You can do that in Multiplayer!
Overall: 8/10 B-

Modern Warfare 3:
MW3 doesn't have a bad single player, but I think they didnt put as much time in, 1 reason is they have been working on BF3 for 8 years. This storyline doesn't make sense to those who didn't play MW2, like me, I just played AlterIW, but it is fairly good, both stories are like Hamlet, almost everyone dies..
Overall: 7.5/10 C+

Realism:
BF3:
BF3 in my opinion is alot more realistic that MW3, remember in the first MW3 Mission, where the building tip falls? Well you cant do that in MW3 Multiplayer, but in BF3 you can. When you look down at your feet in BF3, you see them, when you reload with an empty mag, you have 30 ammo, when you reload without an empty mag, you have 31, since 1 bullet is in the chamber. Physics, Graphics, and weapons are more realistic thanks to Frostbite 3.
Overall: 9.5/10 A+

MW3:
MW3 doesn't have any of the features that I mentioned up there, no Helicopter, planes, and tanks in multiplayer to drive, which I forgot to mention in the BF3 section, none of its more realistic elements are in multiplayer, which wil be our next topic.
Overall: 6.7/10 D+

Multiplayer:
BF3:
BF3 has a far better multiplayer experienced, since there is a much better ranking/attachment system, and there are more mature gamers on Teamspeak, Raidcall, and VOiP. All of those wonderful realism elements are in BF3's Multiplayer. BF3's Multiplayer experience include many vehicles, and amazing and realismtic maps, some from BF2, in the Back to Karkand Expansion/Booster pack. You can use Mortars, Boats, EOV Bots, for a SnD like gamemode, and stab people on the neck from behind.
BF3 Co-Op:.
Co-Op is in this section, since MW3 doesn't have it. (Well in Mw3 its called Survival) CO-OP is small missions to play with someone, based on a separate Storyline, and they are quite fun, and if you do good,you unlock stuff in Multiplayer.
Overall: 9.5/10 A+

MW3:
MW3 has good multiplayer, but less mature players, that what my opinion is. It isn't bad, but it is certainly not the best CoD MP, CoD 4's is. Its less realistic, more n00b-t00bers.
Survival:
Zombie mode where zombies have guns. The End.
Overall: 8.5/10 B+

Awards:
BF3:
Over 80 before it was officially released.
Has won 6 GoTY Awards.

MW3:
Less than 80
Less than 6

Anti-Cheat system:
BF3 & MW3:
They both suck, Valve AC and punkbuster both suck, PB might be a bit better?
MW3 has more hackers.

Overall:
BF3: 9.3/10 A-
MW3: 7.9/10 B-

I was using the MCPS Grading System.
Pictures soon...... As in 1-2 Hours