Why does one have to defeat the other?

Don't have to. My guess is that one is going to come out on top eventually.

Github seems to already be quite on top of Bitbucket. But both can live together nobody has to win or lose.

not necessarily. mutt/pine, emacs/vi, irrsi/chatX, python/ruby, .... in general a good thing.

I still find BitBucket more useful since GitHub has no free plan that offers secure transfers.