Kakashi wins since under normal circumstances Gai would never be opting to die using the final gate and i consider Kakashi to be slightly stronger than Gai without it
Genjutsu won't be an issue for Gai considering he knows how to fight without eye contact
Kakashi is a taijutsu master himself(considered to be above part1 Lee and capable to open at least the first gate), possessing one of the greatest speed and reaction in this manga(reacted to 2susanoo arrows that SM Kabuto struggled to dodge, reacted to Jubidara's counter-assault without no one noticing and even Gaara's automatic defense having time to shield himself, along with many other feats).
6Gated Gai was more or less on par with Jinchurikis in terms of speed and Kakashi was countering them as well, so they were all in the same branch of speed. Where Gai has superior body movement in 6 or 7gate, Sharingan makes Kakashi reacts faster [
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]. It was seen against the Jinchurikis where Kakashi saw the counter-attack faster than Gai with his Sharingan [
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] before both of them blocking the tail [
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]
Hirudora could be an issue though, but Kakashi could dodge it with doton hiding mole [
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] or maybe even block it with a shield(water wall or doton wall [
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])
Kakashi's jutsu speed would be an issue for Gai however. Since it's too fast to be followed [
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] [
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][
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], he can cast ninjutsus without Gai even realising, ending up hiting a lightning clone for example instead. He fooled even high level dojutsu users like Itachi [
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] [
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] and Pain with it, so Gai would have to be careful
But it's said to be a usual trick on him [
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], so Gai of all people should be aware of it and thus not just charging recklessly
He may also use this range attack [
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] in combo with a lightning wolf as well [
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] to gain range and openings. And if Gai gets paralysed, he can easily take the opportunity to snipe him with Kamui
They know each other very well, but overall i just find Kakashi to be the superior shinobi