I don't think Sasuke needs Sharingan to perform some of his Chidori variations.
Sasuke doesn't need to worry about the opponent dodging the Chidori Stream if they're close to him, so that will hit Kakashi.
Base Sasuke and Base Kakashi's Taikutsu are equal. They've fought after Sasuke and Danzou's fight.
Also, who said Sasuke needs Sharingan to use Chidori?
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His vision was blurred then, plus, if Sasuke can do it without Sharingan then Kakashi can. Plus, if you think him using it without Sharingan is only a bluff, see below.
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He was readying his Chidori in order to attack Kakashi but then Naruto stepped in. We all know Sasuke's not dumb enough to let Kakashi evade Chidori, therefore I don't htink he took that risk. I believe he somehow trained his eye to be able to use Sharingan. Of course, if he can do it, Kakashi can too.
In terms of other ninjutsus, I think they would be equal in these as well. Even if Kakashi does supposedly have 1000 jutsus I don't think any of them would be that effective. Plus, if he did have 1000 jutsus he would've shown us at least a hundred of them already. I think they're Taijutsu and Ninjutsu is a stalemate in this fight.
So that's Ninjutsu and Taijutsu out of the way.
I don't think either of them can cast Genjutsu without Sharingan, so my answer is draw.