The Eternal Mangekyo Sharingan > The Byakugan (Possible misconception in NB)
This thread is not to outline how either one can defeat the other but to outline possible offensive and defensive strategies that the Byakugan can use against the Eternal Mangekyo Sharingan (I say Eternal because it would not be sensible to use Mangekyo Sharingan in situations that were not extreme).
Ok here goes :rag: (gl flaming a flame).
Byakugan users do not need to look into the eyes of their opponent, as gentle fist as training demands that they focus on chakra points.
As Taijutsu masters they would only concentrate on the chakra points, especially the fatal blow target, the heart.
Even if they do look into the eyes when Tsukuyomi is about to be cast the Byakugan user can tell as they would see the change in chakra flow, they then should look away from the eyes of the caster before they fall under Tsukuyomi.
Heavenly rotation should repel amamterasu even if the flames consume the chakra expelled from the tech, it is the force of the chakra sphere formed form spinning that repels attacks.
We can see here the ground below Hiashi Hyuga is crushed due to the force.
Shuriken simply repelled.
As Susanoo is pure chakra given form, Byakugan can be used to spot weaknesses in chakra and attack those weakness with chakra expulsion.
An example of this was shown when Neji successfully located and utilised the weak point in Kisames water prison, something that shinobi should not be able to escape from without help.
So yeah I don't think the Byakugan is weak at all.
They may not have perfect Susanoo but remember Madara's chakra is extremely powerful even by Uchiha standards, if someone with astonishingly powerful chakra came from the Hyuga they would destroy mountains also, in fact they would be more unbeatable than Madara.
They don't have much screen time and their tech do not summon gigantic figures or massive massive explosions that can engulf entire villages, but remember the characters that can do this are super powerful main characters
Can do these things.
I think kishi took the Hyuga back for a while because the probably had too much potential so it was kind of like a retcon.
Anyway they are still very powerful as a clan, and can rival the Uchiha.