It'd depend on how you do the comparison;
Game-wise, the CoC would probably win as the mechanics in Skyrim a little more restrictive than they were in Oblivion. But if you can put them on an even footing where the mechanics of Oblivion (enchantments etc) would normally give advantage then I'd put my money on the Dovakhiin.
From a lore perspective, my money goes to the Dovakhiin again. He is literally the only person capable of defeating Alduin, I'd wager the CoC as Sheogorath couldn't hope to achieve that (unless the fight took place in the Shivering Isles, but why would Alduin go there?). In game, shouts are fairly average (I like them) but that is for balance reasons largely. If the lore regarding shouts isn't exaggerated, then Dovakhiin isn't going to have too many problems 1v1 versus any mortal.
The Nerevarine killed 2 Gods (Dagoth-Ur and Almalexia) as well as defeated the Daedric Prince, Hircine. Although, seeing as how evil Vivec turned out to be after the Nerevarine Prophecy came true, i wish we did kill Vivec as canon.
As much as I love Morrowind and the Nerevarine, neither Dagoth-Ur or Almalexia were gods, really.