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Itachi starts with 3-tomoe Sharingan activated and Byakuya starts with Shikai. They can go Mangekyou and Bankai whenever they want.
Rules:
100 yard starting distance.
Both in their primes.
Itachi can see Byakuya and is able to hit him. Therefore, no reiatsu crush allowed.
Restriction on Tsukuyomi, Izanagi, Izanami, and Kotoamatsukami.

Who would win?

Don't restrict Tsukuyomi, Itachi will need it. Since Byakuya is obviously A LOT stronger though, he will be able to break out of it with shear Reiatsu. Itachi would lose though. I think what would happen, is Byakuya would be able to simply go faster than Itachi and use that technique he used on Ichigo to cut his soul chain, but would only cut a bunch of crows. Then, I'd say they would fight, Byakuya might have to use some kido, but could easily kill Itachi with a non-incanted hado 33, so he tries. Then it gets blocked by Susano'o's Yata mirror, then Byakuya says he did well, but will never reach him, uses bankai and evaporates Itachi and his Susano'o. At most, Itachi might be able to land a fire jutsu or something, just because he's so smart and such a good strategist... However, Byakuya has had thousands of years more experience, and is even more of a strategist. Itachi wouldn't be able to land Amaterasu though, just because Byakuya is so fast, and if the Raikage could dodge it, Byakuya could in his sleep. A better fight would be Itachi vs. Renji.