I've just remembered that in the director's commentary Whedon says that originally Baldwin played Jayne 'as big as possible'. I can't remember the exact expression, but basically as a huge offensive bastard like Johnner. Then Whedon told him to change tack. He said 'every character thinks he is the hero of the story', and told Baldwin to play Jayne as if he was the hero of Firefly. I think this direction helped the actor to make more of the part.
It also shows how important direction is, because I think it unlikely that Baldwin is inherently a better actor than Perlman: he just got better instruction about what to do with the same part.