I would like to point out that I am a huge Neji fan, but these battles need logic and reasoning not fanboy opinions of "Neji could win because he's my favorite character".
Both the sharingan and Byakugan can predict movement(yes it can; read the manga. see link below for proof), but Sharingan can copy that movement it see's and use it against the opponent. Which is useless for Sasuke because gentle fist is designed to tenketsu points. It would also be extremely hard to get the jump on Neji because of his Byakugan 360 degree vision can do that haha (but, I wouldn't put it past Sasuke to figure out the weak spot.)
Ok, Lets start off with saying Neji is a taijutsu specialist. Sasuke is a close-mid range fighter. Sasuke being a close to mid range fighter gives him an advantage over Neji because he can go out of range and launch a power ninjutsu against Neji. If not for Neji's Amazing chakra control and abilities he has as the hyuga for example: rotation, he would not be able to beat most of Sasuke's techniques.
If sasuke were to use a genjutsu I doubt it would work on the Byakugan because it can see through almost anything. Advanced genjutsu I'm pretty sure the byakugan could not match against.
Sasuke is highly skilled in all three feilds of combat, which is why he is so dangerous. Where as neji has only high skill with his own clans ninjutsu and taijutsu(from what we have seen anyway).
The other thing to look at is intelligence and observation skills of both of them. For this stat its hard to say because both of them are highly observant, intelligent and are able to see the inner workings of most people's skills and abilities incredibly fast. (Sharigan and Byakugan help a lot haha)
Taijutsu winner: Neji
Ninjutsu Winner: Sasuke
Genjutsu Winner: I really don't think i need to put the name.
This is just a brief summary of my thoughts on this.
Although Neji is my favorite character I don't think he can beat Sasuke. Sasuke just has too many advantages over Neji. Don't get me wrong Neji is nto a pust over and really give Sasuke an exhausted fight, but in the end sorry Neji. Logic and reasoning point to Sasuke!
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