[It isn't. They aren't really rivals at all, because that implies a degree of equality Gilgamesh won't quite acknowledge, no matter what he says to the contrary. Gilgamesh had only one equal in all the world. Masamune may have been fun to play with, fun to tease, to trade barbs back and forth with like this, but they both know he's no match for the King at his highest and mightiest. He's a better sword arm and that's the extent of leeway he's willing to grant.

But it was wrong of him to think that someone like Yukimura represented the truest essence of a Hero. A true Hero pursued his ideals without hesitation, yet also carried with him the weight of the world. He understood the nature of that world. He acknowledged and embraced cruelty in the same breath he would kindness. He understood that, ultimately, Heroes were imaginary things that humans made up to comfort themselves. There's a reason Heroic Spirits only lived on as ghosts. It's because the sands of time would someday swallow them all, even the ruler of their kind, though Gilgamesh won't acknowledge that, either. That he's as much a prisoner as the rest of his kin.

Gilgamesh plays the snake to Masamune's cat. Every flicker of his tail, every quirk of his mouth, he watches, he notes, he records. Even if Masamune wore the scales of a dragon and proudly so, he was only human in the end, and therefore...]

I oversee humanity and tip the scales as needed to set them on the proper path.

[Those same fingers trail up and along his face, cup the side of it to make the perfect portrait for him to gaze upon.]

You are no different. If I am bitten, it was because I was made to be. If I am spurned...

[A laugh. He doesn't even bother to finish that statement, because it's obvious; what does it matter?]