The trailer you saw was actually pretty CoD-ish because it didn't show any of the ways Battlefield is (enormously) different from CoD (which is ****).
Allow me.
In CoD you have ~sixteen players at most running around a small space primarily firing guns at each other and working as lone wolves. You mostly run in circuits around a small network of streets or hallways.
In BF you have 32/64 players organized into squads, sometimes with a commander, running around a huge map with all sorts of pilotable tanks and helicopters and crap, cracking up at the hilarious hijinks or actually making some kind of concerted teamplay with medics, snipers, and engineers working together. It's a sandbox - you can play it straight or do silly stuff like throw all your C4 on a friend's jeep and let him go Jihad Jeep into enemy tanks. You can kill people with power tools or just act as a spotter and throw down smoke to cover your teammates.
In CoD the maps are the same and people camp in predictable hiding spots or strongpoints.
in BF buildings are destructible and if a squad is camping in a building you can bring the whole building down.
In CoD you get pounding rock music and the soldiers are very serious like they're in some ultra hardcore GI Joe unit. You can get killstreaks for doing well.
In BF (Bad Company at least) soldiers swear like sailors and have their own wacky personalities based on what class you're playing. You can get into a vehicle any time you like, no matter how well you're doing.
In CoD a great moment is 'I got all my killstreaks and went 64-3'. It doesn't have much to do with your teammates.
In Battlefield a great moment is 'oh my god, I shot that helicopter's pilot with my tiny pistol and he died and the helicopter crashed into a building and took the whole thing down and crushed 14 of my teammates, hahahaha that was amazing'. Or you could have had a really good round without firing a single shot because all you did was act as a medic.
Watch this. For that to happen in a Call of Duty game it would have to be a scripted single player event. But all of those events, including the chatter, could totally happen in the course of an utterly normal BC2 multi game.