Although I think Hashirama will probably defeat base Minato. But, I will argue for Minato because why the F not. XD
First. Hashirama's Buddha is utterly useless against Minato. It's a short-Mid range jutsu. Minato is small, not a size of the Bijuu, and he can use FTG to teleport to anywhere he wants, so the Buddha is pretty much useless. In addition, Minato dealt with a far stronger jutsu than Hashirama's Buddha comprehension....
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Second. Minato is able to cut the woods, without even using his arms.
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Third: From a 50m, it's probably aspeedblitze anyway. Minato was able to strike a Kunai faster than Kakashi could use
his Kamui, to JJ madara's leg. However, unlike Madara, Hashirama does not have the speed, reaction, or the reflexes to counterattack Minato, so he will most likely get attacked and tagged at the same time.
Forth: If everything else fails, there is always the jutsu that had soloed Hashirama in the past.
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The jutsu can't be seen or sensed, and it deactivates all jutsu. Lol
and there you have it. XD