Marco is someone who believes in the new gen while King is opposed to that. That kind of thing was already established:
King hasnt mentioned the new generation. Momonosuke isnt the new generation.
king is underestimating the resolve of Luffy and company. He thinks killing momo is enough to break their spirits.
marco is saying that even killing momo wont stop Luffy and company.
Thats a difference in opiniom between Marco and King but its not personal stake worthy as far as their battle is concerned.
let me try this with Nami and Ulti. These two also begin with a difference in Opinion. Ulti believes Kaido will be Pirate king, Nami thinks Luffy. But the thing most everyone on the good side believes what Nami said and most everyone on the bad side believes what Ulti said. So this only becomes direct personal stakes between them when Nami defies Ulti at the threat of death to stick to this ideology AND THEN LIVES. Ulti gave her an ULTImatum to renounce the captain or die. She didnt renounce luffy and lived. Ulti’s ULTImatum was broken and now its personal.
See there has to be way more actial interractiom between these Marco and King for this to stick. So far, this is just a difference in Opinion that Marco would probably have with any executive under Kaido