I think in an enclosed space like mirror world Katakuri probably wins as it negates King's speed form and limits his movement while allowing Kata to make full use of his awakening in a confined space.

Out in the open i think King wins. He has crazy range attacks, can speed blitz and spam, .

Katakuri wins! His DF power is more versatile and because he’s also managed to awaken it he’s stacked in all areas of combat! Strength, agility,defense,distance,and speed. Add in his battle IQ,base strength,FS,and fighting skill that made him undefeated for years. King is dead. 😎

King

50/50.

King

While Katakuri hasn’t been powercliffed to an Ulti victim it happened to the point he loses to King convincingly.

Katakuri has all 3 Haki. Simple as that

As much as I love Katakuri and hope that he gets a power up that puts him above King someday, he's not beating King. King's lunarian genetics alone helps him a LOT in this fight. The only way Katakuri is doing any real damage is if he catches King without flames and even then, King is still durable AF. King got this mid-high diff at best until Katakuri gains advanced armament and or advanced conquerors.

Honestly, katakuri extreme diff. He has all 3 haki and a pretty good devil fruit (Basically a logia but without the elements).

@ASimon24 sorry, I didnt know about the rule