Champion of Cyrodiil IS NOW A FREAKING GOD. And not one of those squishy Aedra gods that can die; no, he's a Daedric god. Y'know, the ones that have yet to be killed by anyone or anything, and the type of god that helped Nerevarine get as strong as he is.
"Ya but lyk dovahkiin ken lyk shout rly loud at him n stuff"
No [censored]? My girlfriend's four year old niece can shout really loud too. Doesn't mean I can't kick her ass in a fight, or that I'm gonna shield myself behind her if the devil himself appears in my house.
Yes, however, Dovahkiin can become invulnerable and since we're going off lore rather than gameplay - there would be no cooldown on how much he could use Thu'um. Now, the CoC is insanely powerful now that he is Sheogorath, but we still don't know how powerful Dovahkiin may become in the expansions/ DLC - so I will withhold my final verdict until then. However, as it currently stands.
CoC > Dovahkiin > Nerevarine.