well, at first glance, it would seem that Kakashi would be the one winning since after obtaining both Sharingan and Six Paths Chakra from Obito, he could threaten and harm Kaguya Ōtsutsuki, a god-like chakra wielder. Tbh, I haven't seen Kaguya fight, but from what I HAVE seen in the anime, she was real powerful, pretty sure SHE could defeat Byakuya Kuchiki, but it's Kakashi we're talking about, so I must say we'll need more than this. Kakashi got both eyes from Obito, meaning he can phase through attacks, even if Byakuya is a master swordsman, I must say, Kakashi can read his moves, and you must be thinking, "But Byakuya can use Shunpo!" my answer is, it doesn't matter! Kakashi has TWO sharingans! He can follow Byakuya! NEXT! He has a Blue Susanoo since he got two eyes, a full body susanoo, pretty sure Byakuya can't penetrate that with his sword in normal form... and this is why I said "at first glance" at the start, Byakuya has shikai and bankai, before I start on shikai, one ability of his bankai piqued my curiosity, the ability is Gōkei, basically, what it does is, and I quote, "This form increases the number of tiny blades immensely. It creates a spherical formation of innumerable blade fragments, which swirl around the opponent like a cloud before flying into them from every possible angle, leaving no blind spots and no possibility of escape. It proceeds to collapse in on itself, obliterating the opponent. When used, it completely obliterated a very large building from the inside out, and the resulting shockwave generated by the attack forced Byakuya himself to Flash Step away." no blindspots, and no way of escape, pretty sure that can kill kakashi, UNLESS! He warps outta there! Even if Byakuya uses his Shūkei: Hakuteiken which basically "condenses each and every one of his blades into a single, potent sword, drastically increasing its cutting power. The spiritual energy and pressure released by this form is immense. The blade appears bright white, and its aura takes the form of a bird, earning it the name Hakuteiken (白帝剣, White Imperial Sword; Viz: "White Emperor Sword"). Pure white wings form on Byakuya's back, as well as a halo-like circle, made of concentrated spiritual energy. This form's blade can create aggravated injuries in a single blow.The wings can be used for flight.", Kakashi can read his moves and then use Kamui to warp himself around the blade, so that it never hits him, and when Byakuya is surprised, BAM! Chidori to the heart! (just like Rin, huehuehuehuehuehuehuehue xD) I'd say that Kakashi wins, but then again, there's always the possibility Kakashi can not read Byakuya's moves when he uses Shunpo, I don't know....