In THE WORLD OF STAR TREK, David Gerrold points out that one functional use of the Kirk/Spock/McCoy triad was to dramatize the conflicts that Kirk had to have inside his own head, as a Starfleet Captain. Spock represented the ruthless logic, McCoy the human emotion, Kirk synthesized the two. (Very Freudian, as Gerrold notes: superego, id, and ego.)

By that standard, Holmes and Watson are playing a different game -- the two of them change each other, because Holmes makes Watson think, but Watson makes Holmes more human.