You have to play a little bit to unlock the team-based competitive modes, so you only start out with free-for-all variations of capture the flag or deathmatch. It's very frustrating because people just sit around camping on roofs and have better guns.
I haven't played any of the team competitive stuff yet, but I just unlocked it.
The real fun is "Free Roam". Ride around the entire map and accomplish the bajillions of tasks (hunting wildlife to clearing out waves of enemies holed up in hideouts), or just goof around. It's a little annoying when you get an asshat who likes to kill you or your horse while you're trying to do something, but it's rarely happened to me so far.
One thing that's a turn-off is that the ambient challenges (like gathering flowers or shooting birds out of the sky) have to be completed separately in single-player and multi-player. i.e., the ranks you get for beating the same challenges in sp, don't carry over to mp.
So far it's pretty fun though. I've probably gotten further in multiplayer free roam than in singleplayer.