The only assumption here is that Sanjis fire could be less potent since he is no way a full blooded lunarian if he actually has the genes of them. Kings fire seems more potent as for now.
But anything other than that is facts though. King does fight with anything he has, swords, kicks, punches, he even might headbutt zoro at some point. We shouldn't forget how King in just his zoan form overpowered RS Sanji with ease.