All I've read so far makes no mention of mission based coop, just playing COOP on some maps. There may be objectives, but it doesn't look like there's coop through the campaign.
That may change later, but until that day comes, my money is on Civ IV.
Speaking of which, I just had an interesting idea for a mod for Civ, one that features a cooperative campaign in a fantasy setting. Basically you start your kingdom and everything, and then hordes of something or another invade. It could be goblins, orcs, barbarians, undead, etc... but everyone has to work together with very limited resources against an overwhelming threat. Where do you attack, where to defend? If it's goblin hordes, you have a ton of goblin cities popping up everywhere turning out large stacks of goblin troops. Barbarians would probably raid via sea, be stronger, have less cities, but essentially be like the goblin hordes. Dragons would be singular powerful units that require large armies to take down. Undead, well, they're just undead, difficult to kill permenantly, weak in attack, but they just keep coming and they regenate unit strength in the field quickly.
The normal game would, of course, be the typical fantasy Civ mod that you know will come out as soon as someone can dig into the files.