Where? from the countless hype between the two clans.
One of these hypes are these.
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Those are merely a few hype that the uchiha clan have gained which predate itachi/sasuke or any the current uchiha clan.
In a fight between a 3T user and Byakugan user many advantages that the sharingan has over others is restricted. However due to their weapon mastery, katon + any other jutsu they have/copied should allow them victory. If worst comes to worse the use of izanagi which doesn't require senju dna could be used to decide the fight.
Don't want to get into any sort of vs thread debate
No doubt Neji was stronger than Sasuke, but as you said this was 2T.
Even still with the 2T the sasuke that fought Gaara would give Neji one heck of a fight.
VOTE Sasuke defeated Kyuubi Naruto. The same Naruto who neji lost to, the cs2 played a part admittedly, however once the 3T was awakened Sasuke managed to track his movements.
If we pit hebi sasuke even before absorbing Orochimaru, the one who danced around team yamato is stronger than P2 Neji, even with CS2 restricted.
Yes the sharingan is considered rare even amongst uchiha's, that was stated in part 1. But rather than assuming that this may be due to some dna, it may be and most probable reason for this is because not everybody within the uchiha is a warrior. Some were merely shop keepers and not ninja's so would not have been in a situation where they would have awakened the sharingan.
Think you are assuming that not everybody within the uchiha clan couldn't awaken the sharingan. May not actually be the case as ive explained earlier. The warriors, the ninja's all these to possess the sharingan. From the fodders of the past to the popular uchiha's, to those of the police force all appeared to have the sharingan. So it may be a case of uchiha who don't have the sharingan not being warriors. But you are assuming that just because a hyuga who gets the byakugan by default, is a warrior. Just because they have the byakugan doesn't mean they are warriors, just means they were born with it.
Also nobody is saying that the byakugan makes anybody weaker. Yes kumo tried to steal it, but i actually think that is a dehype of the clan. For kumo to believe they can walk into the hyuga compound and take an hyuga. Perhaps they didn't try this with the uchiha and the sharingan because they knew the chances of a successful mission is next to nil, not that the sharingan doesn't have many admirers.
Anyway ill wrap it up by saying this.
If you haven't noticed kishi has set a precedent. The rarer a jutsu/technique or ability the powerful it is.
This law applies to the dojutsu as well, but also its advancement/power is determined by its requirements
As you said, the byakugan is common. The hyuga's all have it from the start.
The sharigan isn't, but also comes with requirements for awakening.
The ms is considered rarer, but also comes with its requirements.
The EMS even rarer and comes with its requirements
Rinnegan even rarer and comes with its requirements
The more powerful a doujutsu (or technique/ability/kg) is, the rarer it is. But also the requirements needed for it.
Power and requirements/rarity go hand in hand you see. That law has been set
Kishi doesn't do common when it comes to abilities that are considered OP. But also usually slaps some form of requirements needed.
Byakugan is common.
Isn't rare and doesn't need to be awakened
You do the math