In the case of the musicians being more productive, I would have guessed that it's because their creativity fed off of each other, with sharing of ideas and helping each other out of slumps, rather than any urge to outcompete their nemesis.
There's lots of stories of competitive rivalries within bands, and between bands (especially between rap artists in modern age), and between composers/artists. I think there may be something to this desire to one up someone in a creative field when you consider yourselves better than them producing great works.
