I think it's mainly based on game type. For instance, Team Deathmatch, although team is in the name of the game type, doesn't lend itself to teamwork well. yes, you can roll in a group and rip shit up, but I've been the lone wolf with my friends online (who also run as a lone wolf on my time) and we generally won like that. Games like Capture the Flag have more teamwork, but can still be won by ripping through the enemy, grab the flag, rip through the enemy until you reach your flag (Halo does a good job of not allowing you to fire and to run slower with the flag).
Now a game like Demolition in Socom requires your team to get the bomb in the middle of the map (each team has access to it), and then work your way to go plant it (and there are no respawns, by the way). So in that, you have to secure the bomb, make sure you and your teammates don't die or take too much damage, and then work your way to their plant site, which is probably by now quite well guarded. You can even concede them the bomb for the sake of having a better line set up and risking less casualties for the sake of getting it.
I've always felt Socom was one of the best shooters for teamwork, and I've never played Battlefield but I'm glad you showed me that because now I really want to go out and buy Battlefield Bad Company 2. I play shooters like Modern Warfare 2 and stuff without teamwork, but my play time of those games is short lived, because there just isn't any lasting value to it.