Gai > Kakashi in taijutsu. I think I saw so in the official character book (like Gai had 5 stars and Kakashi had 4 or something). I don't know who would win though, but I think Gai would win since he specifically trains to fight sharingan users.

Just note though that Kakashi didn't teach Sasuke Lee's taijutsu, Sasuke had to copy it first for himself then he just trained using it. You can't copy Gai/Lee's taijutsu with just the sharingan he had to train as well (and even then Sasuke wasn't on Lee's level as Gai implied hastily learnt taijutsu wasn't the same).