The lights are on
Things in life are often better when you have a friend in tow, and gaming is no different. Come find someone to watch your back.
in meaning that you would rather work with someone or go all rambo and try to get the best score.
That would depend on the skill of your partner.
If you and your partner are both very skilled players, it's probably in your best interests to cooperate in a co-op game where the goal is to win quickly.
However, if your partner has very little skill or experience with the game and you're not willing to waste time holding their hand, playing to maximize your own success would probably complete the game faster.
Both of the above arguments can be turned around as well. Perhaps you and your partner are both very skilled, but the nature of the game is such that you will complete it faster by competing with one another the entire time.
Alternatively, perhaps your partner is unskilled and the game punishes both of you for the failings of one. In that case, you're best option is to help them at every possible instance.
tl;dr version: There is no simple answer because it depends on both the nature of the game and the skill level of the players in question.