I believe in that state...he would have given Sasuke a run for his money.
Definitely. Just compare their feats.
1) Sasuke attacks Kaguya with Rinnegan teleportation followed by Chidori, Kaguya easily dodges (
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).
- Kakashi attacks a stronger/faster/more powerful version of Kaguya dashing out of his Susanoo with Rikudo enhanced Raikiri combo'd with Kamui phasing effect, aka Kamui Raikiri, Kaguya is not able to dodge, not able to couter, from the lack of "!" until she is hit she is actually unable to even react (
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). there's no excuse "she was surprised because Kakashi phased through her attack" because she witnessed Kakashi phasing through it before, than she had time, she was fast enough to dodge Sasuke appearing at her back with instant teleporting.
2) - Sasuke can't react to Kaguya's S/T Yomotsu Hirasaka in time to dodge it activating his Rinnegan S/T instant swap, let alone dodge on foot (
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). That's even if Sasuke already witnessed Kaguya's S/T speed before (so no "he was surprised" bullshit), (
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), and was able to casually react to Juudara's Linbo, even physically intercepting it.
- Kakashi easily reacts to Kaguya's S/T Yomotsu Hirasaka and uses his long range Kamui to outspeed the teleportation portal and warp away both it and the bone projectile before the teleporting could complete (
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). If one it's not blind, it's easy to see that the black portal that was opening before is magically no more after Kamui warp.
Logical conclusion based on what manga showed (1) = Kakashi's physical speed is a lot, a lot faster than Sasuke, as fast as the Uchiha can be and he certainly is. Kakashi can also add Kamui phasing to his movements, and also Kamui self teleporting (at maximized speed having both eyes together + Rikudo chakra powering; it's basically a free seal-less Hiraishin). Kakashi can also use clones with top notch skill in the area, and spam them due to enough chakra (Obito's + his + some Rikudo chakra) to use Perfect Susanoo without any problem.
Logical conclusion based on what manga showed (2) = If Sasuke is not fast enough to do something against Yomotsu Hirasaka, he is definitely not fast enough to do something against long range Kamui, as it proved to be faster, much faster, than Yomotsu Hirasaka. That means that if both have to attack themselves, Kakashi will warp Sasuke away before he can do anything with Amenotejikara. That means Kamui GG basically. That also means that Kakashi has better reactions/reflexes, so he is much more deadly in CQC (when you have to add better speed, better CQC skill, Kamui phasing and Kamui teleporting, clones with quantity and quality), and he can outspeed and oneshot Sasuke if he tries to do the same. Kakashi is also far smarter than Sasuke.
The only way Sasuke can win is Rinnegan genjutsu, assuming that it doesn't need eye contact, as it actually seems it doesn't. But if Kakashi has knowledge of it, he would use on him his long range Kamui that is faster, or phase to defend. Most of times Kakashi wins with long range Kamui GG or with Kamui Raikiri. Sasuke has more raw power but it's useless when Kakashi can defend with Kamui phasing, and the Rinnegan powers (Deva, Preta and so on) as powerful as they are are still meaningless to Kamui hax, as they can't defend from it and can't overcome his defense. Amenotejikara can't defend from long range Kamui as Sasuke can't react to it, if he failed to do with a slower S/T, and can be defended from with better reactions and Kamui phasing, and also keeping the distance as we know it doesn't work after a certain distance. Kamui Shuriken and Kamui Sword (it's the same logic, just that he has to infuse Kamui powers in the Susanoo sword other than the Susanoo shuriken) make Kakashi's Susanoo > Sasuke's Susanoo, Enton weapons are warped; even Sasuke was angry because of Kakashi's new Susanoo and Naruto joked on him because of that. Kakashi definitely wins more times than not.
On a portrayal note. You have Sasuke, together with Naruto, struggling to fight Kaguya when 2 vs 1, and when 1 vs 1 being outclassed more than once, being unable to defend himself from her, being unable to hit her. Then you have Kakashi, alone, completely changing the course of the fight against Kaguya. The strongest version of Kaguya, don't forget, who he could counter in her giant form (Perfect Susanoo + Kamui Shuriken), who he could dodge and hit in her fastest form (Kamui phasing + Kamui Raikiri), who he could outperform in one of her most haxxed resources (long range Kamui). Then Sasuke gained more Rinnegan powers and more raw power, but they are useless against Kamui, and it's not like they would cope the gap in the last performances of master and discipule. I don't know how it can be said that Sasuke not only has more chances, but would definitely win. Not with what the manga showed, sadly. Only way Sasuke can possibly defeat Kakashi is through Rinnegan genjutsu.