Not easy to determine... First of all they both know each others techniques way too well. We gotta look at everything here, like their fighting styles... Kakashi depends on chakra while Gai is dependent on stamina and we can all agree that Gai has more stamina than Kakashi has chakra (example: Kakashi takes days to recover from spamming kamui his first time, Gai takes a couple hours to replenish from 6th gate first time.) At base their combat abilities are almost equal since Gai found a way to deal with Kakashi's sharingan so we can rule out genjutsu and as far as Taijutsu I'm sure Kakashi could easily keep up with Gai at base stats of course. Kakashi has versatility with jutsu tho but again he would have to keep it to a minimum to outlast someone like Gai. The game changes once Gai goes into gates, and of course Kakashi has MS, I can already hear everyone saying "OMFG Kamui insta-kill LOLOL"... Nah first of all Kakashi needs to focus kamui you think Gai just gonna stand around waiting to get hit? Look back and all the times Kakashi has used Kamui... Apart from Deidara all his other uses he's been standing still focusing... Just look at how much trouble he had focusing against Deidara running and jumping in a pretty straightforward path. Not saying that he doesn't have precision or speed, but it needs to focus and all the fast attacks he's shown teleporting away have been straightforward, and Gai is a fast guy(no puns) he could easily close any distance at 6-7th gate not giving him a chance or he can just avoid it (don't give me bullshit about eye's moving faster cuz we've already seen people avoiding amaterasu which is "instant"). So what I think it'll come down to is Kakashi can win IF he can last long enough for Gai to make a mistake and Kamui him, also he does have raikiri but against Gai's speed in gates I only see it being used in defense to keep Gai's taijutsu at bay. If not I see Gai winning not easily of course but once he opens gates he becomes a much more versatile fighter, we see morning peacock taking out hundreds of sharks and kakashi ain't about to kamui away all that and his hirudora will blast everything, and how are you going to kamui air? Worst case scenario Kakashi deals a death blow on Gai, Gai goes 8th gate and they both die.
