Octane is not the thing making more power. Higher octane = more power is a common misconception, like with your buddy.My buddy would always run 110 octane race fuel thinking he was making more power. We proved it on the dyno that in fact the opposite was true.
Octane is one of the factors which determines how much you can advance your timing (and increase compression) without getting pre detonation. And advancing timing and adding more compression are things that allow you to make more power. So, octane and power are related but not the way most people think.
Purely just by using higher octane fuel in an engine with a carburetor does not increase power. But, in fuel injected engine it might, depending on the software ecu is running.
I run 100 octane (US rating) alkylate gas with mix of synthetic oil. It does not make any more power in my chainsaws than other gasolines. But it has other positive effects on both the saw and myself (clean burn, doesn't go bad etc.).