These two are red headed spear wielders with magical abilities. Each has a tragic past (Undyne growing up with fear of humans all her life and Kyoko... Can't say without majorly spoiling PMMM). They are known for their bad attitudes and harshness to the protagonist(s) early on but later open up to them and accept them as a close friend. The also took it apon themselves the train one of the weakest characters in the verse. One hunts humans, the other hunts monstrous witches. Both can also reach a powerful form near death and are extremely over confidant and cocky but can still be serious when it matters most.
Okay, who I think would win, honestly depends on the scenario or the writers thoughts. Undyne and Kyoko are about similar in base form, but in Kyoko's witch form, she can win. But then the whole including the Undying form for Undyne comes into play, where it was used against Chara in the Genocide run, but doesn't come up in the Neutral run if you kill her. The most accurate assumption is if Undyne thinks something poses a threat to both humans and monsters and then is assumed to be killed she goes into this form. And if Leo decides to include this (most likely because witches are a threat to humanity until slain, and could pose a threat to monsters), Undyne would win.