I've yet to play both. But the gameplays that i've seen of MW3 make me think that I made the right decision not buying it. If I wanted to play MW3, i'll just hop on MW2. Not saying it's a bad game, just looks the same.
They both have their positives and negatives.
BF3 Pros:
- Epic graphics (lighting, destruction, ect)
- Epic sounds
- DESTRUCTION!
- Recoil
- Gravity/Weighted ammunition
- Teamwork
- Epic Moments Online
- Lasting Appeal
BF3 Cons:
- No bullet penetration
- Overpowered Weapons
- Occasional sound muffling (on consoles)
- Occasional freezes of frames (on consoles)
- Slow Gameplay (A lot of people hate, but I love)
MW3/basically 2 Pros:
- Run and gun
- Bullet Penetration
- Epic Moments online
- Massive Community
- Lasting Appeal
MW3 Cons:
- Same as before
- Sounds are meh
- Graphics are good but the same as a game from 2 years ago
- Playing against children not old enough to play the game
- Trash talkers/bitc h players
- Overpowered Weapons
To me, they both serve different purposes. CoD games have always been about instant action. You turn on your Console and bam your in a game killing some people. BF games are slower paced, More tactical, and I think more immersive.
Both DO NOT represent anything close to real war though. And I hate when people think that they do.
Personally i'm a Battlefield fan, have been since the launch of BattleField Bad Company and will be a fan until DICE screws up royally. I love being able to win with my brain, and having to think outside of the box. It really tests your ability to asses the situation and make a game plan based on the resources around you. Could actually help you out with daily life

Yes, I know, crazy.
What I think is better for you? Well, based on the description of what you like. Being good at battlefield takes some dedication. You have to learn to work as a team effectively, learn battle plans, and learn to implement them properly. So Battlefield 3 may not be the choice for you.