From a gameplay standpoint I think the CoC would win, just because you can exploit spell making more in Oblivion than crafting in Skyrim. If we count the Nerevarine in I think MW was even more "exploitable".
Lore-wise we have to ask how do we measure power? The strongest enemy for the CoC was Jyggalag, for the Dovahkiin it's Alduin. Alduin is the World-Eater and can only be defeated by the Dragonborn, in every other case he would just om nom nom his enemy. Jyggy is a Daedric Prince who can only be banished, but Alduin could eat him... so the Dovahkiin killed the more dangerous enemy, I guess. The Nerevarine deafeated a very weak apsect of Hercine and killed two self-made gods, whose "powers" can't really be compared since they were stolen from the Heart of Lorkhan.
Although I don't know why any of the TES 4 and 5 heroes should fight each other. The CoC is the god of crazyness, the Dragonborn fights dragons by yelling at them really loud, I think they would be great buddies.
Not really a fair comparrison. Alduin could only be beaten by a Dragonborn. That doesn't make the Dovahkin more powerful, after all he did use Dragonrend to weaken Alduin to a new level first. We also don't know the relative power Alduin had then and the power he had when eating the world, so that's kinda a horrible comparisson in my mind.
Anyway the thing is if you look at it quite simply then the CoC wil win because he's a Daedric prince, if you ignore that then none of them is automatically more powerful then any other. It depends on the skills learned.