Yes Coop, no Crucible. One thing that really irks me is quickly respawning enemies. It kinda makes the job of shooting them pointless. That's an MMO meme that I dislike. Go to a place, clear a path, find it's closed in behind you. Sometimes Borderlands 20 minute respawn time can get annoying too, but it's overall better balanced.
I think generally I need a sense of goals and completion. Respawning enemies means you can never clear the area, which means can't ever satisfy the goal of 'shoot all the baddies/red dots'. We tried some DCUO the other day, looking for something new to play cooperatively online, and I didn't like it at all. Didn't understand how anyone could like it! Arrive in town, kill baddies, smash poison vents, they all appear back again! A never ending problem with no solution. The goal of these games feels like levelling up, and when I read MMO forums that seems to be how it's played. I don't like that game structure.
For me, I'd want a Borderlands like structure where you form a group of friends and play through a game. That can be open world or tunnel levels, but it needs to be us few, good men versus the world in our own discrete universe.
As for gunplay and stuff, to me it's all much of a muchness from game to game. Not being a shooter connoisseur, I can't tell much difference between one and the next other than gun speed. Tried a bit of Warhawk the other day and it was slow, had a huge dead-zone, and had aiming inertia it seems, so felt really different and uncomfortable. But KZ and Borderlands and Destiny are all the same thing otherwise.