Let’s analyze Byakugan’s powers a bit more. I think it is more than obvious to say that the Byakugan surpasses the Sharingan in all forms of insight.
Some synonyms for “Penetrate/Perceive”:
understand, comprehend, apprehend, insight, discern, make sense of, interpret, work out, unravel, decipher, figure out.
Now look at how Kakashi says that the Byakugan 100% surpasses the Sharingan in this regard COMPLETELY. In other words, in every aspect of penetrative perception, the Byakugan reins superior over the Sharingan. And considering this is a man who has had 3T Sharingan for over 2 decades, and has used them to fight countless enemies and battle, it’s safe to say his words are more than trustworthy.
So let’s look at some of the Sharingan’s penetrative perception feats and abilities. Because of course, any feats from the Sharingan relating to insight will automatically apply to the Byakugan due to what Kakasi said.
First off, people need to understand that Sharingan’s copy ability isn’t merely just some sort of power that automatically grants the user the ability to use the technique.
Rather, it is the keen perception of the Sharingan and it’s ability to analyze and discern techniques that allows the user to learn how a technique is used, such as looking at what hand signs are being used. This is the reason someone like Sasuke still needed training for Chidori and Lee’s speed. Yes, his eyes would allow him to learn how the Chidori and Lee’s taijutsu maneuvers work, but as we saw, he still needed plenty of training to actually learn how to use them. With all this said, does this mean the Byakugan can copy techniques like the Sharingan?
No, since the Sharingan’s ability to understand and it’s ability to copy are different properities. As such, Byakugan would be unable to copy techniques, but it would still be able to figure out how a technique works more easily than a Sharingan.
Next, seeing through Genjutsu.
Sasuke states the Sharingan penetrates and see the reality behind any illusion ei Genjutsu. This alone is proof that the Byakugan, which surpasses the Sharingan in this regard, would easily be able to see through Genjutsu to a greater degree than even the 3T Sharingan. Of course, the scan above also notes that the Sharingan’s penetrative powers allow it to also see the “reality behind spells” as well. Of course, this is very likely referring to ninjutsu and the Sharingan’s ability to discern how the opponent’s technique works and use it for themselves, so this would also apply to the Byakugan as well.
Lastly, the ability to foresee attacks and keep up with an opponent’s movements. It was already stated that the Byakugan can anticipate and foresee how an enemy will move before they move.
Now, how does the Sharingan’s ability to foresee movements work?
As you can see, upon unlocking 3T Sharingan, Sasuke states “With Chakra Sight like this” which makes it abundantly clear that Sharingan’s ability to foresee attacks is based on how it can see Chakra flow. And I don’t think anyone will deny Byakugan’s ability in seeing Chakra in all manners far surpasses the Sharingan’s. This is further cemented when Karin was noted to be able to foresee attacks, and Karin too is capable of reading Chakra flow, with her sensing being superior to even the Byakugan.
Some people may say that Sharingan actually creates images while Byakugan isn’t known to do this, but this doesn’t seem to be the case.
Note that Sasuke says his “mind’s eye”, which is just a fancy way of saying imagining images in one’s head. This basically means these images Sasuke is supposedly seeing are nothing more than a way for Kishimoto to show how foreseeing abilities works, not that the Sharingan LITERALLY allows the user to see images of the user prematurely.
This is also proven by the many, many times Sharingan user’s have failed to avoid, dodge, or counter attacks. Some examples can be found in Sasuke VS Deidara, Kakashi VS Pain, Sasuke VS Darui/Ay, Sasuke VS Kinshiki, Itachi VS Kabuto, Kakashi VS Zabuza, Naruto VS Obito.
If Kakashi can see images of his opponent moving before the opponent actually moves, this wouldn’t have happened, since he would have foreseen the image of Pain ducking down.
Same applies here. If Sharingan truly foresaw actual images of the opponent’s movements, this wouldn’t happen.
You get the idea.
Even Kinshiki, without his Byakugan activated, managed to bypass this. Again, if Sasuke can see literal images, he would have foreseen Kinshiki stepping backwards and countered, and Sasuke even has his sword blocked by him.
Point is, neither Sharingan or Byakugan create images of the opponent’s future movements. Even Zabuza confirms that the Sharingan can’t see the future.
So how does it work? They use their insight and/or Chakra-sight to foresee/predict movements, and with the Byakugan being superior in both categories than the Sharingan, Byakugan naturally has better foreseeing powers. And you have to factor in that Sasuke himself with the jump form 2T to 3T went from being unable to even SEE KN0 Naruto to being able to fight on par with KN1, so that alone should explain how great the Byakugan’s foreseeing abilities are.