I guess you really want me to go into specifics.
Kakashi's Sharingan allow (well... allowed, thanks Kishimoto):
- Sharingan/MS precognition to have enhanced reflexes
- the ability to use Raikiri effectively against high level enemies
- Sharingan/MS genjutsu
- the ability to copy and preempt ninjutsu, taijutsu and genjutsu
- the ability to warp himself to teleport from the real world in Kamui dimension and the opposite
- the ability to one-shot nearly every enemy he could ever face with Kamui, something that made him actually able to contend with nearly every ****ing character in the manga, no matter how strong and powerful
As already said, Kakashi has the exceptional feat to being able to fight on equal grounds, maybe even having the upper hand, with the strongest member of the Uchiha clan, wielding the same power, the Sharingan/Mangekyo Sharingan, but with the big handicap of not being an Uchiha in the first place. And as already said some really strong foes appreciated his dojustu prowess, not to mention that it earned Kakashi's moniker as "Sharingan's Kakashi" and "Copy Ninja" even before that he gained and perfected an asset like a Kamui-equipped Mangekyo Sharingan.
With a non perfected Kamui, as he couldn't control the size and the position of the space-time barrier for his own admission, Kakashi could use an Akatsuki like Deidara as his ***** and then was sure he could have defeated another one like Kakuzu. Some time after, Kakashi was even willing to fight Tobi, believed as the legendary Madara Uchiha, with Kamui.
Some Kamui execution feats:
- Kakashi can canonically warp a human body part in the same time (instant) Obito needs to make it intangible (39)(40)
- Kakashi warps away two Susanoo arrows when both are already at half their way and his Sharingan was still the 3 tomoe one (41)(42)
- Kakashi warps away Minato's Rasengan countered by Juudara really in no time (43), Minato's arm kicked from Madara was hella fast if we think that Minato's body (obviously heavier and so less fast of the arm) went on Gaara so fast that his auto-defense couldn't activate in time
- Kakashi warps away a giant arm of the Gedo Mazo while Madara is already summoning it away with space-time summoning jutsu (44) (Minato couldn't do anything in that situation than ask Kakashi taking care of it)
- Kakashi feints to warp Naruto's Rasengan and then insta-warps away his body before Obito's spikes could hit him, managing to make Obito think that Kakashi missed and he succesfully hit the clone (45)(46)(47). So Kakashi can Kamui away human head sized objects in a more or less instant time and even with fast moving objects/people and unpredictable situations. And he can Kamui away human body sized objects in also nearly istant times, and even giant objects. Thanks to the Kurama's chakra supply from Naruto, Kakashi's Kamui was depicted as a dangerous threat for even the Juubi (48). Just read what is said from databook about Kakashi's Kamui (and that was when it wasn't perfected yet) (49)(50) and what Kakashi says after having faced the Rinnegan and being against one believed to be Uchiha Madara (51). Kakashi's Kamui warped away even Juubi's jinchuriki Madara's Onmyoton Release who nullifies ninjutsu. So... Kamui GG > your favourite character, by feats, and even by hype and portrayal.
Kakashi has also showed that he can warp off from the Kamui dimension the things that he warps in, shooting them out as Obito does, so he can for example warp away a Bijuu Dama or a Jinton, and then re-warp quickly it and surprise the opponent with his own attack. Kakashi can also warp himself with the ability of teleport anywhere he wants, gaining a really useful ability for surprise attacks and for support purposes; for example, he can go to the other dimension, focus his chakra, and then use a giant-size Kamui with ease. Or simply have rest and then perform surprise attacks on his opponent.
Kakashi's Sharingan genjutsu is really strong, it's on par with Obito's as their fight shows, and Obito has some of the greatest genjutsu feats all over the series, as controlling Yaguya + Sanbi, controlling Kurama, keeping Fu and Torune under genjutsu for a long time, reading Konan's mind and maybe even killing her with mental trauma. Also part 1 Kakashi's genjutsu was strong enough to mind**** Zabuza and to make Itachi say that he could have resisted his Sharingan genjutsu, so he had to resort to his Mangekyo Sharingan's Tsukuyomi, having to willingly deplete his chakra and his eyesight without any second thought. Also Gai had to create a special fighting style against the Sharingan's genjutsu just to face Kakashi in their sparring battles.
First of all: remember that until after the chunin exams, part 1 Kakashi was a lot out of shape (52)(53). So what he did to that moment... he could do it much better.
Kakashi has been portrayed as a speedster since his childhood (54), even by Minato himself who acknowledged him as such (55). Child Kakashi before Sharingan could go toe on toe with experienced jonin in taijutsu (56), with two tomoe Sharingan could blitz jonin and rip them in half with Chidori (57).
With a mere kunai in his hand, Kakashi could stop the swing of Zabuza's Kubikirihocho sword (58); he also showed great taijutsu skill (59)(60)(61) and we know that he has always been sparring with the absolute master of taijutsu, Maito Gai. Part 1 Kakashi could also dodge and blitz Zabuza several times (62)(63)(64)(65); if you want to say "well but Zabuza lost his mind at that moment" I think it's true just on a certain point, remember that Kakashi was out of shape, first thing, but was also really exhausted at that point. Kakashi could open at least the 1st Gate (66), powering up his speed and strength, already on really good levels. With a really high level of speed and Sharingan precog, even if he had low stamina, Shunshin + Raikiri was already a S-rank trouble... and in Shippuden with Kakashi's speed feats it became a really dangerous enemy just with the use of his Sharingan, physical speed and Raiton-enhanced CQC.
Beginning of Shippuden Kakashi can easily handle a Shoten Itachi (30% of Itachi's chakra but perfectly equal skills in taijutsu, speed, everything) in a CQC battle, even using a Kage Bunshin. Shippuden Kakashi could dodge a forest-destroying attack (Kakuzu's Fuuton: Atsugai) at point blank and with his attention divided by the taijutsu fight against Hidan (where, even with an injured arm, he was taking care of him with ease using just a mere kunai against his scythe), keeping up with Kakuzu's masks and taking an eye on team 10 (67)(68)(69) ... and right after that quickly intercept Kakuzu's fast Raiton ninjutsu with Raikiri, saving team 10's asses (70). With a little distraction, Kakashi could blitz Kakuzu who didn't even perceive his fast attack (71), even if we know that Kakuzu has so fine reflexes and perception skills that he can perceive Shikamaru's Kagemane (who obviously doesn't make any noise) approaching his back (72). It's worth note that Kakashi attacked so fast that even Hidan and the team 10 members, who were facing Kakuzu and so had free sight of what was happening behind him, were completely surprised. Kakashi could nearly blitz Asura Path with his raw speed, dodging his attacks and appearing at his back (73)(74). Kakashi is so fast that he was paced two times with Gated Gai (75) and managed to counterblitz the V2 who were ganbanging KCM Naruto and Bee landing Raikiri on them (76). Kakashi, right after regaining his mindset, outreacted and outspeeded Obito (77)(78) who had the same physical speed of no Shunshin KCM Naruto (79). Kakashi was also called fast by Obito when he quickly appeared at his back (80). Kakashi also proved to be faster and better in CQC than Obito more than once (81)(82)(83). Kakashi could also canonically move and react at least on par with Minato in physical speed (84)
Kakashi tanked like nothing a surprise Domu-enhanced kick from Kakuzu that send him flying for metres away and breaking some giant trees, or a couple of Shinra Tensei, and didn't lose consciousness even from the 3rd, as Choza (one who could jump in between Asuma' Katon ash ninjutsu like a boss) did. Kakashi also fought a lot of times with wounds and injuries without his performance being hindered. Kakashi can also wield the Kubikirihocho with just one hand with great skill and for hours, and his physical strength is so high to make Obito internally bleed with just a couple of punches. Also as said before he can stop a Kubikirihocho swing with a mere and small kunai.
Part 1 Kakashi couldn't follow Itachi's fast jutsu execution, but he could react to it showing great execution speed too, and he could perfectly understand and counter his combo (85), something that Hebi Sasuke couldn't do: sick Itachi could make a KB while exchanging shuriken with Sasuke and Sasuke didn't see it, and later was surprised (86); a more healthy Itachi tried to feint and surprise Kakashi with bushinjutsu, but Kakashi reacted and countered with his own bushinjutsu (Kisame also noted that Kakashi was fighting pretty well) and then even understood who was the true Itachi and who was the clone (87), wasting his opportunity to attack to save Kurenai from Bunshin Daibakuha. Part 1 Kakashi's reflexes and jutsu skills were above the ones of Hebi Sasuke in Shippuden and we know how fast and reflexive Sasuke was.
Shippuden Kakashi showed astonishing reactions in the Kakuzu/Hidan fight, against Pain, against Sasuke's Susanoo and then in the War Arc. Kakashi tracked KCM and BM Naruto's speed and insta-Kamui'd his attacks in the same time that Obito used his intangibilty (chap. 596), or manage to fool him in mere instants (re-read 598), these are some crazy feats. He can canonically react at least on par with Minato (88) but seemed even better than Yondaime, if we account that here (89) Minato is hit two times (in between his sliced arm is also kicked away) without being able to react and Hiraishin away, but Kakashi, even if he could absolutely not be prepared for what happened and was clearly surprised, could activate and execute Kamui in a millisecond, warping away Minato's Rasengan countered by Madara (90), and that Kakashi, even in an exhausted state, could perceive and mentally react to Juudara's speed (while Minato couldn't, if he could have he would have activated Hiraishin to teleport away) (91).
Kakashi is said to be smarter than Shikamaru (92) and the best in analyzing skills (93). He outsmarted people like Zabuza, Itachi (for his own admission (94)), Pain and Obito, who had to recognise his smartness (95) and quick thinking and acting (96). He is one of the smartest ninja in the series, arguably the smartest one.
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That's where I copy pasted it from. Also, sorry for the numbers. Go to the link to see what scans the numbers were referring to.