Honestly I don't think God of War would be the best comparison, because Kratos tends to get stronger or weaker depending on Rule of Cool or how plot relevant it is.
I feel like The Legend of Zelda games would be a better comparison. Both Link and the Champion start out as normal villagers with pretty wimpy stats. They both fight through hoards of enemies and go through dungeons. And they both end up in a final showdown with a god-like magic demon, Ganon/Lethice.
Also the Beautiful Sword heavily mirrors the Master Sword, since you get the Beautiful Sword so early and in such a unique way and it's one of the most potentially powerful weapons in game it's worth pointing out
I'd say at their strongest, they could both be considered demigods, they've both taken down entire armies and beaten up dragons, but not without considerable effort. I don't see them destroying a city without more than a bit of exertion.
Though if we're talking about the Champions real strength then their real power is in their ability to transform and adapt. Because tf items affect humans so much more easily than other races they have a huge advantage. Consider the fact that the Champion could have wings to fly, a prehensile tail to trip enemies, powerful hooves to kick with, 12-inch horns to gouge through flesh, natural armour to protect their skin and a pair of venomous fangs. The Champion could adapt their body to deal with potentially any enemy type. Which also means enemies can't prepare in advance for what the Champion will attack with.
Then the Champion can even disguise themselves as anything. So if there was a legion of imps coming to attack them, the Champion could transform themself into an imp, sneak into their camp and then poison the imps' food while they slept.
TL;DR: Basically I think the Champion could beat anyone in a one-on-one fight, once the opponent wasn't ridiculous, anime levels OP, and they could easily wipe an army of well trained fighters. But with their adaptability, unpredictability and potential strategic advantage the Champion becomes much, much stronger.