What does it matter which group of nobility Skyrim's peasants pay taxes to for the next couple of decades?

The taxes don't matter, what does matter is putting forth a unified front next time the turbo-fascist Thalmor-controlled Aldmeri Dominion tries to invade. As the Thalmor themselves put it, it really doesn't much matter who wins the war, all that matters is that the war ends. Either side winning is bad for them.