Gai is experienced with fighting verse Sharingan users, he can look at the feet and fight them.
Gai being a 'mainly' Taijutsu based ninja also gives him another advantage.
To beat Gai, Kakashi will need to finish the fight quickly, the longer the fight the worse it becomes.
Although Kakashi can use his normal Sharingan alot longer, once he uses Mangekyou, and it doesn't finish the fight quickly, he's over.

I think this would be a rather close fight, considering they are 'Eternal Rivals', Kishimoto wouldn't make this fight a flawless victory.