Susanoo-Neji could cut through threads that not even sasuke could. Sasuke had to use the most powerful offense(as stated by kabuto) in order to burn them away. Therefore a byakugan user could cut through Susanoo or use his byakugan to find the weakspot and penetrate there. Since those threads were considered unbreakable and to date they're unbreakable that means jyuutsu a technique only utilized by Byakugan users can break through susanoo since susanoo is not unbreakable.I agree with the amaterasu and genjutsu one but i just dont see how the byakugan can counter susanoo or kamui these have to be the most Haxx techs in the series while byakugan was trolled in the second series i would say byakugan>sharingan in naruto but on shippuden sharingan jumps above maybe even the strongest dojutsu in the series other then the sage rinnegan and juubi and older son eyes.
Basically its like comparing Neji to Sasuke Itachi Obito or Madara IMO Neji cannot beat any of them those are the strongest ninja to ever wield the sharingan and he is the strongest bykugan user so that why my vote goes to sharingan.
Kamui-The byakugan allows the user to sense attacks coming. This isn't a vs thread in respect of (this character > uchiha) but rather why the byakugan is better then the sharingan.