What if Carrot and Weatherwax come to conflict? how would that end up?

Say captain Carrot and Granny weatherwax came to a conflict, where they both wanted different things and their was no real way of them both getting what they wanted, in that battle of minds and will, how do you think itd go?

Carrot has his true king charisma and granny is a headologist, carrot is simple like a sword, to the point he doesnt really get fumbled around or tricked, because he is too simple for them, too much to the point, while granny mostly relies on getting into the other persons head, which with carrot is a place not even the narrator can get into.