The idea wasn't to have them compete. The idea is to have "dissimilar redundancy", so that the US still would have a human-rated launch system with the ability to go to the ISS in case one of them gets grounded for whatever reason.
And besides, the purpose of aerospace spending on human spaceflight isn't just for the purpose of human spaceflight, but also for related capabilities.
And in any case Russia's entire space program is at risk of going under given the budget issues they're going to be dealing with.