This is a fierce battle of legends since Minato and Hashirama are both very powerful. Hashirama has several ninjutsu of incredible size and power, which would prove to be tough to stop. That being said, he may have gotten a lot of hype and a sound reputation, but a good deal of it occurs from off screen feats. Minato is more of a speed fighter and he has a lot of powerful abilities as well. His teleporting jutsu can turn the tides in battle and he is able to augment his physical strength to top things off. Hashirama will not be able to defeat him, but it would be a very close fight. Minato wins.