I think yamato is around king level. If they both fight it could end either way. I don't think that yamato is much stronger than king. Just because he is fighting hybrid kaido doesn't mean that kaido is fighting him seriously. Yamato is his son and he wants him to be shogun of wano. Thats why he doesn't fight yamato with full power.
Fuck it. Since Yamato fanboys and this fandom in general can apply their headcanon to everyone they want, here’s mine:
King is awakened with advanced CoC, advanced CoA, and his fire is more potent than the Mera Mera without the weakness to magma along with multiple form changes like Chopper but he never has to use them because he is unstoppable at base to anyone not top tier level
I think they're comparable. I expected Yamato to face Kaido to break the bonds they shared but I didn't expect her to do so well (though, while I think it's one of, I wouldn't say her current performance is the best against Kaido). If Yamato doesn't show anything more before going down and King reveals impressive stuff against Zoro then maybe King but I think they'll remain around the same strength regardless of how stuff goes.
Yamato holding kaido albeit kaido not using his full power is still highly impressive ; King got very good hype -- Unique race but yama has mythical DF which kaido even hypes up. Tie for now until we see more of either of them