genjutsu works by attacking the brain directly and then influencing all the senses, including chakra-related senses. the byakugan-user might have an advantage compared to fodder-nin because he might be able to actually catch sight of the chakra moving the air towards him(and his brain) and can rwact according; but once hit, they'll probably be another victim depending on the genjutsu-level and whatnot. The sharingan has been specifically stated to be useful against genjutsu, probably due to its mirror-like nature, which can even reflect the genjutsu back on its user.
Karin, also seems to imply that she would be able to tell if she's under genjutsu or not, but again, that can be due to her specific chakra-sensing ability, i forgot the name of the technique, but it has something to do with an "inner eye" if i remember correctly.
i always wanted to se ehow a byakugan-user fairs aginst genjutsu, but kishi hasn't provided a chance.
i too look forward to see what's the deal with neji.