Mkay, here's how i think it'd go down, Ryu wud go in with a swooping swallow straight away and cut the prince in half, Then after seeing his body suck itself together he'd start to formulate a tactic. He'd start running circles around him, running along the walls circling to the top of the arena where the prince can never catch him because his wall running ability clearly isnt on par, while running around the arena he'd be throwing many an expslosive shuriken, one or two or more wud have to be life threatening, forcing the prince to use more sand, when ryu thinks the time is right, he'd jump off the wall and try to swooping swallows the prince again moving so far and so fast in one move he'd be out of danger regardless of slow mo. Then ryu uses his magic conscutively while the prince uses his time changing buisness, ryu cant be hurt while using ninpo, he's then probably out of sand by the time that ryu's out of magic if not ryu's got an inventory of items to help him out, he'd just leave it so the prince is gonna make his final attack with the slow mo time thing, then he'd stand there, turn to shaddow just as he makes his attack (ghost like) appear the other side of him and sevre both hands from his body and his head in one strike, there's no way in hell he'd be able to go back in time from an instantaneous strike cutting off the nerves in his neck and also detatching the muscles in his hands. Hell im not a ninja and i can work out a pretty solid tactic against the guy, just imagine what ryu wud really do.
This is all theory and speculation, nobody here's right, but to be honnest I dont see how ryu wud loose, regardless of the princes time abilities.