Mmm Gonna write a long wall of text
First i am gonna underline some common errors i've saw in the discussion
1) mokuton can't control tailed beasts: it can only restrain them, in a similar way to kushina's chakra: the evidence is in the fact that the kyubi had to be sealed in mito uzumaki after shodaime defeated madara
2) When Madare faced SHodai he did not have mokuton, rinnegan and perfect susano: those powers probably come from the fusion of uchika dna vs senju dna
3) it is wrong to compare edomadara mokuton use to hashirama's one: i've seen people stating: spam mokuton bunshin then jukai koutan ecc ecc
Madara did this because he was and edo tensei and therefore he had infinite chakra
4) when shodaime faced madara he had alrdy given the tailed beasts to other villages therefore he faced madara alone
Let's analyze both hashirama's and minato's features: to simplify the things i am gonna use a scale from D to A++ (d,c,b,a,a+ ecc ecc)
Hashirama: Offensive power:B/A mokuton is not the exactly the fastest attack around( naruto could speak to kurama, summon clones, form rasengans and counter the jutsu before it arrived) and probabily doesn't istantly kill a guy when it comes in contact: isee minato easily evading being choked or grinded by wood as long as he has some seals placed somewhere
Defensive power:A/A+ Mokuton must be able to stand to Madara's Normal Susano, probably the TTB and the massive force of kurama
He also should have some kind of no seal heal jutsu, but as long as we don't know if hashi used some kind of seal ( like tsunade) i expect it to work like kabuto's one ( Naruto vs Kabuto) even if in a better way and supported by way more chakra
Speed:B Nothing special there
Chakra reserves:A++: i expect it to be about 150%+ of naruto's ones
Intellingence: B/A I don't think he is stupid
Minato
Offensive power: B
Until we see some spectacular tech the best offensive jutsus minato has is his rasengan which is about the size of an odama rasengan and the food chart destroyer tech, both supported by the usage of FTG
Defensive power: A Space-time barrier, FTG to avoid dmg
Speed: A++ no brainer
Chakra reserves:A as shown by the fight between tobi and kurama minato actually posseses very strong chakra reserves, comparable to naruto's ones
He teleported Kurama, two tailed beast balls, summoned gamabunta, kept kyubi in place while kushina was giving birth to naruto, rasenganed tobi, contract seal on tobi, eight trigram seal on the kuybi, shiki fujin and FTG
Intelligence: A+ no brainer: great analytical skill especially in stressing moments
Let's go ahead to the fight: i see hashirama shaping the battlefield to his own will but unable to land a killing blow on minato as long as he spreads kunais and seals and keeps FTG away
AT the same time the only way for Minato to kill hashirama is to cut his head or rasengan him in the face, the other damage he can do can be healed at least 3-4 times ( not more assuming hashirama does not store chakra in some seal)
I see chakra reserves of both the hokages going down at the same rate: it is true that hashi as more chakra than minato but the mokuton surely takes out more chakra than the FTG which is used to evade the former
It all comes to whether minato can tag hashirama or not: if the shodai gets tagged he is dead since minato can simply keep slamming him with rasengans until he has no chakra because shodai won't have the reflexes to react
If minato charges frontally i can assume shodai has the time to wall himself
The genjutsu is, imo, unuseful as minato would simply FTG away
I say 50% minato 50% shodai