The Byakugan surpasses the sharingan in terms of insight. But sharingan can copy any jutsu no matter the chakra nature. And it can also see where the other persons body is going to before 2 secs quicker, which gives them time to dodge.
So that makes them equal. But when the sharingan reaches MS or EMS for that matter, the sharingan is in a whole new level. With the doujutsu and all...
Unfortunately this is incorrect
Byakugan surpasses Sharingan in chakra sensing, vision and chakra control,
this is because they can see at near 360, can see chakra flow, can see for miles and can control their own chakra points flow possibly better than any other clan.
As the best sensor types in NU getting a hyuga to Fall under a Genjutsu is near impossible.
Byakugan surpass sharingan in Taijutsu completely.
Sharingan surpasses Byakugan in all jutsu analysis because their eyes can follow movements better than anyone else and their minds can process that information faster than anyone else.
They surpass hyuga in Genjutsu usage due to the genjutsu techs that come with their tomoe.
Sharingan surpass hyuga in Ninjutsu completely.
See they are very different, Rinnegan is even more different, I will admit it does seem like the source dojutsu of both of them (since it allows the user to master all elements easily, as well as great chakra control), but I do not think they are just simpler forms.