My favorite is Halo. Halo 3 specifially is the pinnacle of console fps gaming. Halo: Reach and Halo 4 were, for me, step backs though multiplayerwise. Still great games, but I don't really like armor abilites or random weapon spawns.
I wish more console fps games had a feature similar to forge. It just adds so much replayability. Not only that but the level of customization of game modes is crazy for a console game. Those are two things I wouldn't mind if other developers copied more often.
I don't have too many friends that play PC shooters, so I don't get as much enjoyment out of them, but my favorite would probably be Left 4 Dead 2. If i can manage to find a good team to play as and play against versus mode is ridiculously fun.
Xbox Republic Minion