Higher octane burns slower.
You can look at it however you want and octane does NOT add horsepower. If you are tuned for a race fuel mix to need 97 octane, then thats what you need to not get knock. If you modifiy the car and are running more boost than pump fuel can handle, then all the octane is doing is preventing knock so the KR doesn't kick in.
Hate to triple post, but I'm going to give you a perfect example.
I've got a good friend with a highly modified 3000GT VR4. He dyno tuned it to a very conservative pump gas tune of 520 whp at around 15 psi, if I remember correctly. He could crank the boost the 30 psi and run 116 octane and see 700 whp.
Did the octane add horsepower? No, the additional boost added the power. The octane only prevented knock so he could run at that power level.