When i first saw this i was like holy crap Ryu would win. But then i realized Hayate has some powerful techniques of his own, like what is shown in the opening of DOAU. Hayate also has access to the same type of bows and arrows Ryu uses; the ones from the military. I’ll post some videos of them doing some awesome stuff. Ryu and Hayate have about the same speed, have powerful ninpo, can teleport and appear anywhere they like, etc. In a sword fight, Ryu would have the advantage. Ryu has the Dragon Sword which, after fitting the dragon’s eye in it, turns into a weapon of immeasurable power. Plus, Ryu is a descendant of the dragon lineage and has fiend blood running through him. While turning into a fiend, Ryu got a dramatic increase in strength. Ryu could even take slashes from swords, seeing as they’re nothing like the power and magnitude of the True Dragon Sword. So, in a sword fight Hayate would most likely get slaughtered. In hand to hand combat well, they’d tie. In DOA3, they fought hand to hand and they seemed about equal to each other. In a sword fight, Hayate could win if by a miracle he happened to shoot Ryu with an APFSDS arrow, or if he teleported behind him and assassinated him. Though, that’s unlikely. Also, Ryu has elemental magic which also gives him an advantage.
If this is Ryu with just the Dragon Sword, then he and Hayate would tie. Their ninpo power is about equal though i think Ryu’s is slightly more powerful. In hand to hand combat, they would tie also.