The Gaige one is the only one with a bonus character (and that is the extent of the content). Haven't played it, but most people seem to like it.
Then there are 3 mini-expansion DLCs, each of which has about a dozen maps, a main storyline, and a bunch of side missions. Oh, and a couple of optional raid bosses for people that like that sort of thing.
The first one (the pirate one) has a great setting, and some entertaining characters, but it has an irritating habit of giving you a main story mission that sends you through a map, then on completion, giving you a side mission that sends you through the same map, in the same order.
The second one (Mr Torque)is extremely silly in an over-the-top 80s pro-wrestling kinda way, but it's probably got the best writing and gameplay.
The third one (Big Game Hunting) is probably the weakest. It has some really pretty maps, and some different looking fauna, but the story is really half-assed, and a lot of enemies that are really annoying to fight. It's easily the most skippable one, if you're buying ala carte, but I think the season pass is good value (assuming you like the base gameplay) especially with a 4th DLC coming out at some point.
Oh, and there's an extra arena (Creature Slaughterdome, I think) It's cheap junk, but if you like the arena fights from the main game, it might be worth picking up on sale. (It's definitely not worth the $5 that Steam is showing as it's normal price. Maybe $2).