At first I was thinking that Minato would win it easy, but after thinking more about it im not sure, infact im not even sure he would win the fight, but im also not curtain that kakuzu could win it either...
first if all I would expect that Minato propertly knows nothing about Kakuzu (and if he did I don't think it would be more that what village he used to be from, and that he primarily uses Earth techiques) and I would expect Kakuzu to have more than minimum of intell on Minato (I'm sure someone have put a bounty on Minato's head, and even if no one did that, he was or would have been a very famous Ninja in his time) I just can't believe that Kakuzu would not know anything about "The Yellow Flash" (he was feared by allmost all non Leaf shinobi) most Ninja was told that if they ever saw him, they should turn around and run from any battel, no matter how close they wore of winning it.
So I see it as very unlikely that Kakuzu would not know that Minato is regarded to be the fastest or at least on the fastest shinobies in the world, though I would also say that the propability that he knows of the rasengan, is slim at best.
So this fight pretty much comes down to how fast kakuzu can release his Masks (I expect that Kakuzu would have 4 masks before he would go up against another hokage, I don't see him taking unnessesary risks) and if Kakuzu can release them while he used his "harden skin tecnique" and how fast he could get his ultimate defence up compared to the speed minato can place his kunai's on the battle field, and also if kakuzu uses the element of surprice (ambushing Minato with his masks already out) which I would say is propertly what Kakuzu would do if he got the chance to do it (again, I just don't think he would take unnessesary risks against a Hokage, or any other strong Shinobi)
We also have to take in to account the chakra cost of Minatos flying god technique, and how much chakra it costs to use the Rasengan (and if it even can penetrate Kakuzu's Jutsu, I personally don't think it can) though we also have to take in to account the location of the battel field, will Minato be forced to redirect attacks that could hurt people from the leaf, like he did with the 9 tails Tailed Beast Bomb (if Kakuzu chose to attack him in the leaf village, there is also the added risk of Minato getting back up from the Black Ops or other Jonin rank Shinobi) or if it's a place where Minato just needs to dodge the attacks, do to there being no one around to get hurt?
Also If It was Minato on the other hand that got the jump on Kakuzu I can't see how kakuzu could win the fight, there is a 50% chance that his deadly fire/wind combo would be ruined even before the fight had begun, and even if those 2 masks wore still intact it would still severily lower his chances of succes of winning. (if kakuzu stands still with his tecnique active, and the fire and wind mask have combied, then minato only needs to dodge 2 masks at the same time) Sins Kakuzu can pretty much be ignored while Minato focuses on the Masks, sure Minato can't penetrade Kakuzu's defence, but Kakuzu can't fight back either, It's also likely that Minato would try and get the masks to hit eact other or Kakuzu, and if the Lightning mask managed to hit Kakuzu the match would be over (or Kakuzu would at the very lease lose a heart)
And even if the fight drags out for long and Minato managed to take down 2 or even 3 of the masks I'm not sure if he have the stamina to take down all Kakuzu's 4 heats...
So I would expect that at some point in the fight Minato would simply chose to use the Flying God Tecnique to escape the battel do to the lack of chakra and therefor making it a draw...
