Being a top competitor is almost impossible to measure. Kiki does have some excellent points in his above posts.
I guess you would want a top competitor playing for you if the fate of the world is at stake.
Without picking any one myself but many have picked Pancho Gonzalez when this was asked and some Jimmy Connors. Others have picked Lew Hoad.
Look at Djokovic in recent years, he's won a lot of matches from match point down. The man refused to give up. Same with Nadal in refusing to give up.