I know that cutting contests are a big part of jazz mythology, and players often tell these stories, as Lades reminds us.  But I confess to a growing irritation with this gunslinger mode of competition that produces perceptions of winners and losers.  That's why I find this story told by Harold McKinney (of the large McKinney family of Detroit) so refreshing:

Harold recalls when Sonny Rollins came to Detroit in the late 50's as the hot young tenor player.  He went looking for Yusef Lateef, older and established in Detroit.  As Harold describes it, Sonny came into a club where Yusef had just finished for the night.  In fact, he was on his way to his car.  Someone came running with the message that Sonny Rollins was looking for him.  (Jazz version of High Noon.)  So Yusef went back to the club for the showdown.  Sonny started with a blistering barrage at an impossible tempo, creating gasps among the few onlookers left, then stepped back and waited confidently for Yusef's response.  Yusef had maintained that gentle, serene, introspective demeanor of his during Sonny's pyrotechnics and when it was his turn played a very slow, sparse blues, using few notes but conveying a great depth of feeling and maturity.  His soulful story captivated the onlookers in a very different way.

According to Harold, when Yusef finished, everyone turned around to look at Sonny, but he had left.