Gai trumps Kakashi in raw power, endurance and overall physically however what he lacks in his physical nature he makes up for his mental capacity (intelligence) and his overall balance as a shinobi.
If you look at in terms of a shinobi who is the better? My vote goes to Kakashi. What I mean is, Kakashi is an overall well rounded shinobi. His ninjutsu game is perhaps one of
the best in the series. He doesn't have too many of those special OP skills but he has perhaps the largest and most versitile arsonal of techniques we've seen. Kamui is probably his only over the top technique which gives him the edge in a fight but Kakashi has something for just about everything we've seen. His range of techniques is great.
His taijutsu game up there too. There isn't one doubt in my mind that Kakashi can keep up with the skill levels of any shinobi, Lee and Gai included in a taijutsu fight pre-gates of course.
Genjutsu, his Sharingan gives him the advantage in that allowing him to see through it for the most part, we've seen little of his abilities in genjutsu but from what we have seen and what the data tells us, he's above average in that category.
On a physical plain Kakashi isn't even that bad either. He's definately quick and he's strong, I mean he's still relatively young, what early 30s.
Kakashi is more rounded then Gai is as a shinobi.
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What Gai has though is a level of raw brute strength that shatters charts and that's the only thing that will keep him even considered on the same plain or greater then Kakashi for some.
But there's a thing about the gates people don't understand which affects Gai's endurance and stamina. Gai is long lasting without the gates, the gates strain him and he can only sustain them himself for approximately a few minutes. It's like Naruto in Sage Mode. He's left exhausted after that so just saying Gates, Gates, Gates like Gai can do that all day everyday is false.
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In my view, they're how they've always been portrayed in the series, as equal rivals. People who keep insisting that people who say Kakashi> or even = to Gai are fanboys but lets that's their own fanboism talking for looking only at power level. Those who are stuck on the Gai>>>>Kakashi because of Gates obviously forget how Kakashi fights. Against a guy like Pein, who Kakashi had vastly inferior info on then Gai, used a clone from the get go to determine his abilities and potentially weaken him. What makes people believe that Kakashi will fight guy, a close personal friend of his for several years who he's fought, and fought along side of, head on.
Gai insists he knows how to fight against a Sharingan user by looking at their feet, but that's defensive on how to avoid genjutsu and for somebody like him that's good, but you can't block out the Sharingan's perception. Everthing Kakashi sees with his eyes he can predict his opponents move. Non-gate enhanced Kakashi can keep up with Gai no problem with standard Sharingan perception. Gai has nothing to deal with blocking the visionary perception of the Sharingan like Zabuza. Gai's skills in Ninjutsu are below jounin standards. He has one technqiue we've seen. As for his genjutsu abilities, Gai can release non dojutsu genjutsu and knows how to avoid dojutsu based gen at Kakashi's level.
Gai needs Gates to defeat the arsonal of ninjutsu, and superior skill Kakashi has over him in all fields of the shinobi with the exception of Taijutsu. When Gai passes the third Gate he's stepping bounds past Kakashi then, however, even if Kakashi doesn't have the speed at that time to keep up with Gai, Kakashi has the intelligance enough to avoid Gai for the durration of the time he's in the gates.
What plays to Kakashi's disadvantage is his level of chakra. When Gai is going beyond 4 or 5 Gates Kakashi's going to be blowing through everything he has just to avoid any sort of contact with Gai and defending. Kakashi will be on the defense at that time because there's very little Kakashi can do to harm him, with the exception of Kamui which requies visual sight of his opponent. Kakashi's not wasing Kamui like Naruto blows through his chakra, because he doesn't have the reserves for it. By the time Gai is rearing his end of his Gates, he's going to be just as, if not more so exhausted then Kakashi and at that time both shinobi will be fighting on will power.
Kakashi fights smart and has the versitility of skills. Gai fights strong and hard and he has the reserves to break through physical barriers. The two are Yin and Yang you have The Yin (Kakashi) balancing the Yang (Gai) and both shinobi are equals...
Oh and Kakashi's fighting ****ing Bijuu right now, give this guys some credit for ballz people.