For me, World of Warcraft is definitely a cooperative game. I've never really been a competitive person, and I always like seeing people around me succeed rather than fail. I enjoy PvP sometimes for the challenge of it, for working out the problem of how to win a battle against intelligent opponents, so it's true that I also like competition in moderation, but things like rankings and phrases such as "I pwn your face!" mean nothing to me.
Some people I know, though, just thrive on the thrill and the glory of smashing their opponents into bits, melting their faces, and generally causing mass depletion of health in all who oppose them. Others have been captivated by the next big upgrade, and they really love the feeling of achievement that comes from acquiring gear that few others have.
Which is more important to you? The joy of united cooperation, or the thrill of competitive glory?