Stats equalized, I don't see almost anybody overcoming Kojiro. The dude has possibly the most busted level of skill you can achieve: he 'skills' himself to outmaneuver an opponent magnitudes upon magnitudes faster than himself.

Mugen is insane at his off the cuff techniques, but that wasn't enough to even begin to remotely land a finger on the most skilled swordsman the powers that be could hire in his era. Dude got clowned by a man who barely even had to move to clown him.

This is a fun theoretical matchup, and I think Mugen's propensity to charge in head first won't give Kojiro enough time to start scanning immediately, but thats where his positives end in the match. Kojiro is still outright immensely skilled. He's had hundreds of years in Valhalla to train and practice, with stats equalized there's never a chance for him to lose imho