When compared to games like COD, it is the more realistic of the two. Of course it's not 100% realistic, or it wouldn't be a videogame, but when comparing the two, BF easily comes closest to mimicking realistic situations than COD does. I haven't gotten into MW3. I played it and thought it was crap like MW2 was. I'll be happy to get into COD again when Treyarch releases their next title. Battlefield is more fun than COD in terms of playing as a team. There isn't one game mode in COD that I've ever played where there wasn't a "hero" at some point. Someone who just ran and basically carried the entire team. Battlefield isn't designed to have heroes like that.
When compared to Unreal Tournament, CoD is pretty realistic. Basically you are comparing two games that the developers never claimed to have any sort of realism. When Battlefield 1942 came out and become popular I honestly was baffled. Yeah it was fun but just the year before a game had come out (Operation Flashpoint : Cold War Crisis) that had a lot more content and features and is still one of the few games with a sense realism in it. Bitter I am, but if Battlefield was realistic. It wouldn't be popular.
I suppose realism has different tastes to different people then. What exactly are you looking for with the term "realism" when it comes to videogames?
There are several games that have what I enjoy when I'm looking for more serious gameplay. Red Orchestra 1&2, Joint Operations : Typhoon Rising, Op Flashpoint : Cold War Crisis, Arma 1&2( and 3 when it comes out),and Swat 3&4. I play Battlefield for getting pistol headshots from a few hundred meters, and messing around with friends(I have all the pc ones except bf3). Basically CoD but with bigger maps and vehicles.