Rinnegan = Best at Ninjutsu
Sharingan = Best at Genjutsu and Taijutsu
Byakugan = Best at ???
There are 3 techniques, Ninjutsu, Genjutsu and Taijutsu. And Byakugan isn't best at any of them.
Sharingan > Byakugan in Taijutsu because Sharingan allows the user to predict their movement.
So basically I don't see the point of Byakugan. It doesn't have anything unique like the Sharingan and the Rinnegan.
The Byakugan allows for Konoha's strongest taijutsu style - Jyuken.
Taijutsu goes to the Byakugan, not the Sharingan.
The Sharingan is more tuned for genjutsu.
That's what it's known for.
Rinnegan = Ninjutsu
-Mastery of all 6 elements
-Absorbing any type of chakra-based attack
-Summoning numerous types of animals without limit
-Gravity/Repulsion Manipulation
-Removal of souls upon contact
-Reading minds upon contact
Sharingan = Genjutsu
-The power to put whoever looks into the Sharingan into a genjutsu
-High caliber genjutsu techniques such as the Tsukiyomi and Koto Amatsukami when you reach the MS
-The Sharingan also has skills in certain Taijutsu via muscle prediction, but when it comes down to it the Sharingan is
known for it's genjutsu - even the basic 3-tomoe Sharingan.
-When facing an Uchiha, you don't worry about what ninjutsu attack they'll use or how they'll approach you with taijutsu. You worry about looking into their eyes because you fear their
genjutsu.
Byakugan = Taijutsu
-Ability to see the chakra network and the tenketsu
-Enhanced vision to neutralize almost any surprise attack
-Ability to use Jyuken - Konoha's most powerful form of taijutsu - to directly damage the internal organs
-The Hyuuga themselves are taijutsu specialists who are close-combat fighters. This in itself supports the fact
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I know there are areas in which the skills of these eyes cross over. The Sharingan can be proficient in taijutsu, the Byakugan can be used to sense genjutsu, and the Rinnegan is practically the daddy of both eyes. What I'm emphasizing is the areas in which these eyes particularly specialize. Not all of the things they can do.