Kakashi barely have any feat that can drive Neji to the corner. His long range jutsu such as waterdragon isn't sufficient enough to impale Neji Defence, furthermore Neji also has air palm and vacuum palm to counter his attack. Air palm can instantly hit the vital point which it destroy inner organ and that move cannot be avoided once a user locked on a target.
If Kakashi get's close to the opponent, he cannot beat in hand to hand combat, Hyuga are the strongest taijutsu, and the byakugan definately have better insight and sensory capabilities than his 3 tomoe sharingan so therefore he can anticipate Kakashi tactics and his movement and obliterate Kakashi with his gentle fist.
Part 2 Kakashi is the same except that his only caliber is Kamui.