Kaido took lots of G4 ryuo enhanced attacks and shrugged it off with mild internal damage only, King can't do that; King get's washed badly by that level of attack.
Zoro's tatsumaki grazed Kaido in one spot that instantly regenerated (after unleashing Enma properly), and Kaido was distracted trying to swallow Luffy, not on full guard with his wings in cross block fashion with CoA and flames used to mitigate the damage.