I don't remember it being cartoony. 

I just checked all the games mentioned by people so far, and the game I'm thinking of doesn't seem to be any of them. If this helps, iirc, you never actually saw any characters in the game, it was all just cars/tanks.

Well, there was a game called "ThinkTanks" that came digitally to XBLA, too. Maybe that's why you can't find it.
https://www.youtube.com/watch?v=xVUeGCSvRZc

Oh that's def Nintendogs.

Are you absolutely positive that it was tanks and not mechs? Or that there weren't vehicles other than tanks? Because the list of games that feature prominent tank combat is absurdly small and none seem to match what you're looking for.

If ThinkTanks doesn't fit the bill:

I'm not going to watch gameplay or confirm coop, but here is a list of mech games that may be right. Just try hard to remember if you're mixing together details from other titles. Very few people have a perfect memory, and the more vaguely you remember something, the more likely you are to get even the most basic details incorrect. That said:

Battle Engine Aquila
Gun Metal
Gungriffon Allied Strike
MechAssault
Phantom Crash

None of them quite sound exactly like what you described from the vague and lacking Wikipedia descriptions, but the list of games with vehicular combat is already small, and the number of mech games are small enough to fit in a single not all that big Wikipedia article with every other vehicular combat game.

It must be Phantom Crash or Spy hunter. Good games.

Actually it might ha e been Smashing Drive. I remember that had power ups a lot.

The game you are talking about reminded me of BattleTanx: Global Assault, which is for PS1 and N64. It has Coop and the tanks have special abilities.

So I'm not 100% positive it was tanks, but it was definitely vehicles with wheels, so no mechs. Things like armored cars maybe?