Also, the Curse Seal. It grants increased strength, speed, chakra potency and the ability to grow freaky hand-wing things. Also grows out your hair (which Neji doesn't need, any more would just be a hassle *cue L'Oréal hair toss*) and gives you what looks like a natural coating of lipstick (Neji might've liked that function).
What does training under Gai grant again? Well, growing wings seems unlikely. Chakra potency is countered by things stated in my earlier post, especially if tenketsu-closing carries over to CS mode. Neji has also fought it before, so it might not be quite as game changing as people seem to think.
EDIT: Wasn't the Byakugan what discovered Danzo's use of Kotoamatsukami, the supposed "ultimate" genjutsu? Not even a trueborn Hyuuga at that...
yes, but byakugan also didn't even notice that tobi had the same eye as kakashi.