I've played both for the same amount of time since their release, and it's different depending on your style of play.
Looking for quick matches where you can run around, run-and-gun? MW3.
Looking to slow things down a bit and be more strategic? BF3.
The problem is how each company has approached DLC, at least on one of the games. MW3 introduced DLC packages through their COD Elite service, which still only bring maps to compliment the game. Meanwhile, EA has shown DLC superiority so far with their Back to Karkand expansion pack which not only bring maps but also weapons and vehicles (I'm not saying game modes here because there have been free updates to COD that brings in new game modes like Drop Zone), something that I've wanted from COD DLC - something else besides maps. That's why I liked it when Treyarch was doing COD because at least their DLC had a Zombies map in addition to the four maps. Not to mention I'm a PS3 owner, so why am I going to pay the same $50 for a year to get the map packs later? I would of considered getting it in the first place if there wasn't this Microsoft/Activision exclusivity in place.