Poison, plagues, invisibility and laser/explosion spam provide him some opportunity to hurt Katakuri. Even if it's just chip damage over time.
That'll turn this into a battle of attrition and a dinosaur has the advantage there.
Katakuri's own AP is also very unimpressive, and Mogura isn't worth all that much when Queen can additionally shield himself with hardening.
Queen has low chances though, if he doesn't have decent speed to effectively fight back.
Katakuri is still probably the favourite, but I'm hoping that Queen gets decent feats to enable me make a case.