No that was obviously in respect to Naruto's intelligence..You can clearly see that in that scan.
Minato praised Sasuke here first in regards to his intelligence and also told Naruto how the Jutsu worked
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Yes, clearly he was referring to his intelligence here though it's important to note that he was not making any comparison between Naruto and Sasuke at that point.
Naruto then showed his intelligence by applying what Minato said which you can see from Sasuke's reaction upon having the flashback of Minato saying that..Then Minato praises him right after Sasuke remembers implying that it was then intelligence aspect of it
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What did Sasuke do or what did Naruto do that led Minato to refer to reactions or speed if that's what you're trying to say?
That had to do with Naruto's combat instincts as he was able to instinctively react to Juubito's attack which allowed him to save both Sasuke and himself. Minato made the comparison as EMS Sasuke managed to intercept Juubito's attack despite having to create a longer reaction in comparison to KCM Naruto, but the fact that KCM Naruto managed to react to him somewhat is what warranted Minato's statement of Naruto keeping up with Sasuke.
No..Naruto actually ran out of KCM upon trying to use a BD
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Except we've seen Naruto in far worse circumstances such as when he collapsed against Kimimaro, but still maintained his cloak or when Naruto's KCM was depleted after confronting Itachi and Nagato despite being able to create multiple clones and use KCM extensively. Naruto clearly could use KCM, but him attempting to apply the correct Yin-Yang Ratio and release more chakra than he was used to (as he believed a full-fledged Bijuudama is what would overcome the 3rd Raikage) is what caused his disruption of chakra to occur which thus led to elimination of his cloak.
Evidence?
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As you can see, him attempting to use the Bijuudama led to him disrupting his cloak, but if you pay attention a few panels afterwards, he managed to use it just fine. He could clearly use Kurama Chakra had he wanted to considering Kurama's Reserves far surpasses Naruto's. As long as he has his own Chakra (which he does as he was capable of using Sage Mode), then he can constantly depend on Kurama's Chakra, but Sage Mode was more ideal as Sage Sensing enabled him to react earlier as his perception of speed increased which enabled him to react more effectively.
HM has superior sensing but KCM has better reactions for sure...Best feat of HM is reacting to the 3rd(Around V1 Ay in speed) while best feat of KCM is reacting to V2 Ay who's obviously much faster.
Superior Sensing ultimately leads to superior reflexes as the Sensing aspect of both modes enhances his reactions in his Base State.
SM Naruto not only reacted to the 3rd Raikage who might be on par with V1 Ei's speed (for simplicity's sake, let's say he is), but he reacted to him while charging head-first and still evaded at the last second. KCM Naruto wasn't even capable of doing so. Everytime he charged at V1 Ei with his own speed, Ei managed to easily intercept him.
Furthermore, KCM Naruto managed to react to V2 Ei's Shunshin due to him moving in the same direction as Ei which changed his perception of Ei's speed as Ei would appear to be moving slower. Even then, he didn't manage an offensive maneuvor and strike Ei before he could react like SM Naruto did to Sandaime Raikage making this comparison useless.
Sage Sesning being superior doesn't actually mean HM has better reactions. KCM showed better reactions as well.
It does. While I am aware BSM Naruto has superior Sage Sensing due to being able to draw in more Natural Energy, my comparison is just to display how Sage Mode allowed BM Naruto to perceive Juubito's movements which are a lot faster than BM Naruto's and even react to him. The same thing can be applied to SM Naruto as he utilizes the same type of Sensing, but his ability to perceive movements would be in relation to Base Naruto (if that makes any sense at all.) Because of this massive increase in threat perception, he can easily react to his opponent at the last minute and even form his reaction earlier than KCM Naruto can which yields a great increase in reactions.
I'm not trying to force the idea that SM Naruto's Reactions blow KCM Naruto's out of the water, but I do feel SM Naruto's should at least be better by a decent margin.
False and I gave reasons above.
Refuted.