This is a tough one. Its pure Taijutsu vs pure Ninjutsu basically.
-Gai: Totally out does every oppponent in taijutsu, its a simple fact. I also believe he can hold the 6th gate for a long period of time(he has been doing it since the start of the fight against Tobi).
--The hardest thing for Gai in this fight, is if he is smart enough. Gai has the strength using Evening Tiger could win it and could possible destroy 2-3 hearts, and morning peacock can kill 1 or 2.
--Kakashi got Kakuzu to go into close combat and Kakuzu is arguably barely better than Kakashi in that field... So Gai should be on whole nother level.
-Kakuzu has a lot of powerful ninjutsu attacks that can cover a large range and is easily one of the best stragiest in all of Naruto. He could probably figure out Gai's movements quickly and counter attack. But his iron skin is worthless in this fight.
--If he can out think Gai and trick him, Kakuzu can win this
---Long story short both have a chance to win this. Gai can speed blitz to win this with 6 lethal blows to win, or if Kakuzu has time to think up a plan then he can win.
For me its 70% win for Gai