In a game like Skyrim I focused on the campa--well that's not true either lol.
Bad example.
I generally do the campaigns first and then look at multiplayer. Although for Assassin's Creed when Revelations came out I was strictly multiplayer for a long time.
I guess ultimately it would be a little of both, like I said it depends on the game.
It depends on the length of the single player. If its a standard FPS, then i'll beat the SP first. If we're talking about a 20-30 hour long campaign like Red Dead Redemption or Mass Effect 3, then its both.