"Winning is Everything" isn't what Vince Lombardi said. The exact quote is "Winning isn't everything - it's the ONLY THING". Competition is one of those duality words - what I mean is some people thrive on it and think it is the essence of civilization and others feel it can bring out the worst in humans.
I fall into middle with a leaning toward the real benefits of competition. Can competition bring out the best in you? And what are you really competing for --- what is the end goal?
I remember an exercise in the Covey training we did at Accenture where we were teamed up and asked to "Win as Much as you Can" as the goal. What we discovered in the game is that there was a way for all the teams to win more with certain actions - however the first competitive natural action was contrary to this potential outcome. It took a different view of the goal (and cooperation with others) to make the end result happen.
You can compete, cooperate, and co-habituate. There is an outcome of Win/Win.