There are many, many, MANY differences between Modern Warfare 3 and Battlefield 3 with their online multiplayer offerings. Perks, destruction, kill-streaks, vehicles and more all differentiate the two games to provide a unique experience each.
It's MW3's twitch-shooting vs. BF3's larger, more focused wars. One slaps you in the middle of the cross-fire and the other at least gives you a breather before riding into a hail of bullets and frag grenades.
While all this is true, there really is only one key difference between these two - the time it takes you to die. Observe...