Really thats ur proof? His appearance changed?
By this logic when naruto transformed into KN0 in the forest of death he was more powerful than KN0 used against neji because of the eyes
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Yet based on limted feats and how the two modes were used and the power showed , there is ntn to suggest that the red eyes is stronger than the chakra mode , quite the opposite really
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When used against neji the chakra was so much it wrapped around naruto's body to form a chakra cloak which was able to guard against neji's rotation and protect him
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The reason red eyes lost to 3T Sasuke was due to not having a chakra cloak which could expand to extend reach and protect against sasuke's hits , even so he managed to land a glancing blow on 3T sasuke by cuttin his cheek
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If KCM rushed him like that he would have been sent flying or be forced to rethink a CQC fight since he lacked defence.
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And even so the cloak was able to protect naruto from neji's rotation which knocks chakra away which means it could also protect from sasuke's katon similar to this
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Naruto series is all about match ups , if naruto used red eyes mode against neji then he would surely have an easier time than sasuke would against KCM since red eyes has no protective chakra wraped around him to challenge neji's rotation since at this point it was kurama's chakra vs neji's chakra
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If red eyes rushed neji in a similar way then he gets pushed aside neg diff.
So again i ask wat makes u so sure that red eyes mode has more chakra than KCM used in the chunin exams?