All dragons are kin of Akatosh.

Also, if the dragonborns first shout misses, then the Hero of Kvatch has an opening.

Anyone can use a shout if they learn and train how to. The Dragon Born has the ablility to absorb this knowlege from the dragons themselves, and thus bypass all the time it takes to learn it.

I never got the sense that the Champion of Cyrodiil was any one special other than the fact that they happened to have been at the wrong place at the right time. They don't have any special inborn powers or the like and while true that they become the new Sheogorath, it's stated in-game that it's only in title and not actually power. True, it's implied that Sheogorath in Skyrim is indeed the PC from Oblivion but it's not outright stated and in my opinion that little comment he makes about the Oblivion Crisis felt more like a simple shout out to Oblivion rather than a direct statement of fact. So, who would win in a fight? I'd have to say it'd be the Dovahkiin. They have an inborn ability to shout. They have dragon blood coursing through their veins. They are blessed by Akatosh. The Champion of Cyrodiil is just some random dude who was good at killing Daedra.

And going off that, who do I feel would win in a fight involving the Nerevarine? Well the Champion of Cyrodiil is already ruled out. Dovahkiin may be blessed by a god, but the Nerevarine has killed gods. The Nerevarine has gone toe-to-toe with the Daedric prince Hiricine and bested him in combat. The Nerevarine is blessed by Azura and his Corprus Disease makes him immortal as far as age and disease are concerned and for somebody who has killed gods and wields legendary artifacts like Keening, Sunder, & Wraithguard, I just have a very hard time imagining them having died in the ~230 years since Morrowind. That's a whole heaping of ass kicking experience right there.

Hero of Kvatch because mine can jump from one side of Cyrodil to the other and also his horse has armour, does Dovahkiins, I think not.

The hero of Kvatch because he is lord sheogorath and could easily massacre the dragonborn.

Me, 'cause I get to close the topic for post limit.