Both modes can be funny (costume).
But the most time competetive pisses me off cause 99% of all players uses M9 with Rate of Fire, KAL7, Micro with RoF and Revenge! Also it laggs really. Costume Games are very funny. I love Competetive Matches with/against 5 friends as Costume Game.
The most time I'm searching for public games (and thats very often) I search for Cooperative Arena 'cause it makes fun. Play as a team against CPU's and that. And when I play Cooperative Adventure I think that I play Campaign with friends.
Public: Almost just Cooperative
Costume: Very often Team Deathmatch.
Sorry if my Post is unreadable, I'm just a german from Naziland