Yes, it's about creativity. But there's no getting away from the competition factor. Just look at the way Divas sharpen their claws on each other's reputations... To be serious, though, I suppose my point was that if you can set aside the aggression, you can get something really special going on where 'rivals' can bounce their talents off one another in a very positive way to ever greater artistic heights. I would argue that many duets, for example, gain their strength from being competitive as well as complementary.
Let's begin with the Three Tenors. They have all sung some of the same roles and they do them each in their own way. Despite the fact that the 3 Tenors phenomenon is not to my taste, I would say that part of your question is already answered in the very fact that they are collaborating.
But to get more to the heart of the issue, any singer who has a career in opera must know that collaboration is the bottom line as far as achieving a great performance.
As in any kind of music, it is all about ensemble.