In BM you get to have better sensing,more chakra,stronger chakra,Better durability,kurama avatar and the cloak basically works as a mini shield against average attacks
More chakra (access to Kurama fully), presumably faster because of more Kurama chakra, chakra sharing, much better durability, access to Bijuu dama, access to Kurama avatar etc.
KCM is when Naruto draws on chakra from kurama but the chakra itself is not tethered to kurama,it's basically Naruto using the kyuubi's chakra without the actual kyuubi there. The same difference between a main generator and a back up generator. BM is when Naruto is pulling chakra DIRECTLY from the kyuubi and not just a limited supply of his chakra, BM can also manifest the actual avatar unlike KCM which is usually there when the kyuubi is not there or if Naruto is unable to access the kyuubi directly as usual.
BM Naruto is Much faster, Can manifest Kurama Avatar, Has more Raw Power at his disposal and every physical stat is buffed up to a level higher than KCM.
The official name for BM is Kurama Mode. Here's what I've noticed. Now, I'm not sure if there's an increase in chakra power, but there's
A. and Increase in speed and/or more control in speed.
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Naruto in Kurama mode surprised Kakashi and Guy with how fast he is despite the fact that he fought alongside them in KCM. This would imply that he increased his speed usage upon getting Kurama mode. Also, KCM Naruto has little control over his speed, which is why he probably gets cornered by the likes of Obito (but never has this problem in Kurama mode)
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B. Naruto demonstrates far better chakra control in Kurama mode.
KCM:
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Kurama mode:
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Naruto needs a clone in KCM to form a TBB, but can do it one-handed in Kurama mode.
This made me legit laugh, cuz of how true it is Lol
Also, I made a thread about it before, but all I got was speculation. People just assumed that he gets stronger, faster, and better sensing capabilities... Leading me to believe that there really is no difference besides the fact that the Kurama avatar is manifested. Naruto himself gains no actual enhancements