I think that, while elite athletes all have a competitive streak, there's a lot of natural variation in personality as well. Larry Bird may not have been an asshole off the court, but if you were guarding him it was a different story.

The other thing to note is that, as long as you avoid doing something stupid like throwing people through plate glass windows, it's easy for PR to do a lot of magic. Most people never realized what MJ was really like while he was still playing. Brett Favre was kind of a dick, but it took most of his career until that was found out. Ultimately we don't know what these people are really like. Who knows what lies behind Tim Duncan's placid exterior?