I'm not used to debating with Naruto characters, so I'm probably wrong, but I'm pretty certain that Neji has the advantage here, especially considering that you restricted one of Kakashi's strongest attacks, which makes him pretty useless here against a guy like Neji, and this is part 1 Kakashi so he is even more restricted back to average-below average chakra reserves.
Neji seems to have better Taijutsu, and in CQC he is much faster with his attacks. He also has better defenses as seen with his Rotation. He has the Byakugan to make up for sneak attacks around him that Kakashi might throw like his water or fire jutsus, and he has rotation just in case Kakashi might want to try those underground sneak attacks, as that wouldn't work as long as Neji has his Byakugan activated.
Part 1 Kakashi would be exhausted after using the 3T for just a little amount of time, as seen with his battle with Zabuza. Neji can surely outlast him. Everything Kakashi has is knocked back with rotation, and as seen in the war arc, Neji's Rotation was shown to be on par with Hiashi. His air palm can come in handy too and can keep Kakashi at bay.
It would also be disastrous for Kakashi to even think of countering Neji up close as Kakashi would just get destroyed by his Gentle Fist, so the only way for Kakashi to win is by keeping his distance and throwing ninjutsu, but even that is pointless as Neji's wide range of vision is not falling for long ranged ninjutsu and Kakashi has no other way of hitting Neji.
If Kakashi wants to engage in Taijutsu, he gets annihilated. One palm to the heart, and he's dead. One hit at his chakra points and it's over, and he has no way of unlocking them. In this case, Kakashi is slower than Neji in Taijutsu and has worse Taijutsu than Neji. Neji can easily either dodge his Ninjutsu or just block them with Rotation.