Zen, random, and I did some coop last night.
The mission based coop is basically the same from U2.
The Coop arena is a mix of siege mode (gotta hold a point and only kills inside that point gets you money and stuff), survival (what it sounds like), and gold rush (again, what it sounds like... you gotta get one treasure across the map.)
There's 10 levels to the coop arena and a 20 minute time limit. You win if you do all 10 within that time limit. Also, enemies get harder as the levels progress. At one point you get sneaky bastards who do nothing but try to butt rape you. And their attack overrides your melee, so it's really freaking cheap.