I still havent gotten a chance to play the Single Player, but I will soon. I doubt that the MW2 is better. Honestly the MW2 Campaign was good, but I expected more.
Battlefield has always been more technical than CoD. Here you can't go running around shooting people like crazy as you would in CoD. This is a strategy and team oriented game (as all Battlefield games).
Now the reason for that grenade not blowing up the shed, is due to Destruction 2.0. For example, in BC1 you could knife a wooden fence and it will destroy all of it. Here, however, only a chunk gets destroyed. You can make holes on walls to poke your gun out and shoot through there while still having the rest of the wall covering you. Its because of this, that the shed didnt blow up completely, throw a rocket launcher at it and I'm sure you'll see it in pieces.
As for blowing up houses in BC1, you can still do that here. Matter of fact, here you can bring the building down to the floor and destroy it completely. Oh and it does not disappear, you will see the debris laying there for the rest of the game and you can climb and hide within the debris - a good tactical idea to sneak around and be hard to spot.