I am in a similar position. I don't mind playing with random people, but not against.
When I play co-op against the computer, especially games that tag you to tasks as complex as "reach the end of the level, and kill everything on your path" (like Left 4 Dead, Borderland or Resistance 2), then even noobs can cooperate to archieve the goal...
When I play competitive, I know I am the noob that didn't spend +100 hours to reach level 50, unlock everything and knows the best places to get headshots in every map and the best weapons to do it. I understand that for some people that is the goal of the game, but for me its just about having fun.
By the way, one nice exception I find recently is NFS: Hot Pursuit. Its competitive online, but it only matches you against your friends, which makes it more personal (and fun) that just trying to beat some random guy...