If Sai goes up in the air with ink birds, Neji can't hit him but Neji has rotation to nullify Sai's attacks so they this would be a long fight.
Sai does have the ability to use ink clones which will be useful for diversionary tactics to allow Neji to open up his guard and then attack him with ink beasts from Neji's blind spot.
Neji still has full body blow so if an ink beast tries to bind him, Neji shoots chakra out of his body to destroy them. Vacuum palms give Neji a decent mid ranged offence but they won't reach Sai in the air.
Sai will most likely eventually win with high difficulty.