in my opinion Minato is superior to Hashirama. Talking in a count the the highest of power they showed, so what does that mean is I'm including Kurama in Minato's arsenal as well. :amuse
First of all, base Minato is much faster than Hashirama as was proven by the manga (Regardless if you believe it's FTG or not) as we can see here that he arrived before the other Hokages [1][2]. That's beside his obvious advantage in term of speed, so there is no need to go in depth in this regard.
Now, the second important point is the fact that Minato can separate his Kunais quickly and effectively we saw that when he covered a huge area around the Juubi [1][2]. Even Tobirama who was hailed as the fastest shinobi praised him for that [1]. Now, as far as I know, hashi does not have any jutsu that as big as the Juubi or the area around it (notice that Minato did it base) so, having Knaui far away all around the battlefield is going to help Minato a lot to teleport for any case when needed. We also know that Minato uses tons of Kunais when fighting, examples of that would be [1][2]. He uses that to attack or dodge the others' attacks, and for example he dodged A's attack who was considered to be the fastest shinobi [1][2]. Therefore, dodging Hashirama's jutsus should not be as hard since they are not as fast, and we saw the Gokage getting out of the WoF area of effect rather easily [1][2]. It's just madara attacked them after that and forced them to return to the jutsus' AoE, even with that Onoki was able to stay awake and destroy it with his Jinton.
Now, unlike the Gokage, when Minato teleport Hashi can't possibly know to where he's going to teleport, so he can't use the same thing that madara used to force Minato to go to its AoE. Not to mention the TBB has a greater power than Onoki's jinton, so it shouldn't be hard to blow it up completely.
Another thing that Hashi has is his gates to pin down the others like he tried to do that against, Juubi, obito, and madara. However,
that won't work very much for him here because. 1- Minato can teleport himself. 2- Minato can teleport anything touches his chakra, and 3 he can use S/T barrier to redirect it before it hits him. So, I'm really not seeing much of what he can do with that.
Hashi clones are fodder's level as proven by madara [1] (not to mention they have no feats anyway).
Also, Minato is a sensor and he can know about the clones as shown before [1]. Not sure if I can use this, but since Minato is a perfect Jin he should also be able to sense the emotions as Naruto & Mito, if that was the case, then that just erase any chance to Hashi's clones to fool Minato.
Hashi has also his genjutsu, but I'm not sure how is that going to help him here, Minato is a perfect Jin and he can sense as well, so the genjutsu is basically useless against him.
Another thing of Hashi's jutsu that has a great AoE is his Nativity of a World of Trees. As great as it seems, but this jutsu has been defeated at least 2 times. The first one by Hiruzen [1] and for those who are planning to say "No, Hashirama was weaker" too bad, because first of all Hiruzen was also weaker than his prime self, and second he showed the ability to destroy even the god Tree's roots [1][2]. So, unless you think Hashi's wood are superior to the Tree's then that's not an excuse. The second time, Naruto's clone was also able to destroy it with some rasengans [1]. Now, for Minato he can use different methods to deal with that. He can use his FTG to teleport to somewhere else, his shunshin, TBB to blow it up, or his Rasengan [1][2][3]. The Rasengan was able to destroy the chakra arms (which was enough to destroy the Hokages' barrier) and even damage the black rods. Also, another thing to consider is even if Hashirama was able to catch him, Minato can simply teleport as he did against the god Tree [1][2]. If Minato and Tobirama can have seals on a safe place [1][2] which can be several KM long [1], it's not very rational to think Hashi's jutsus who pales in comparison will cover all the places to the point there won't be any seal on safe area! Not to mention that after Hashi uses his jutsus the remaining woods will not be used in the battle afterword as we saw in the battle between madara & Gokage for example.
Another thing to consider is Hashi has also some great defensive jutsus like Quintuple Rashōmon & Hōbi Technique. The first one may be very good to protect him from from a TBB that fired off in front of him right away as we saw in the manga (The TBB did not explode though), so it may protect him if Minato used a TBB in the same way Madara did, but what if Minato teleported behind him or somewhere else and used it against Hashirama, how would he deal with it in that situation? What if Hashi did indeed manage to redirect the attack with his jutsu, but Minato teleported back at him? Because if Minato used the TBB that means it does have his chakra, and in that case he would be able to teleport it [1][2][3].
So, even though Hashirama has those good defensive moves, it's not guaranteed that they will work the same way they did against madara, since Minato's fighting style and abilities are different.
Another jutsu of Hashirama is the Hotei Technique, honestly what is the point of this anyway? Even IF Minato somehow was not able to use his shunshin and they were able to catch him, what stops him from teleporting? Or he can use his own chakra arms
[1][2]. I don't really now how can this help.
Hashi also has his wooden human, and wooden dragon, which he usually use them together. Although, the wooden human may seems great and all for being able to stop PS swords, but we haven't really seen any offensive abilities from it, have we? Also, the wooden Human and wooden Dragon were blown up by the TBB as we saw [1][2].
So, even if the Human guy returned it (assuming Minato won't teleport the TBB out of its hand) the explosion will still finish the wooden human, while Hashi will survive, but even Kurama has a great defense as we saw against the Juubi's TBB [1]. That beside given Naruto the power to redirect 5 TBBs..etc. Notice that was not even with SM.
Now, we also saw the Wooden Dragon got destroyed by FRS and Naruto's war speed [1][2]. so, it shouldn't be all that hard as well, that's if we assumed the wooden Dragon will catch him anyway.
The only thing let in Hashirama's jutsus (that we know of) is his Buddha. I honestly don't see how would that work against Minato exactly?
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Minato can teleport it away with S/T barrier just like how he did to the Juubi's TBB which was bigger than the Buddha by far. Or, if that's so hard to believe, what strop Minato from teleporting behind the Buddha and uses his chakra arms to touch the Buddha to teleport it with FTG?