Of course higher octane gives you more power in the engines designed to use it, otherwise there would not be different grades of gas. When you use a lower octane fuel in a high performance high compression engine the ECM has to retard the spark to prevent knocking at times and you do not get the rated HP. You may not feel it in the seat of your pants but a dyno will show it. Air craft engines use 100 octane for a reason. Using premium gas in a low compression engine designed to run on 87 octane will not give you more power. Yes 87 is cheaper gas than premium grade and is for a reason. Try pricing aviation gas. There are three grades of gas according to the EPA.

For fun look up Top Tier gas, it goes over and above the Minimum EPA requirements for detergents and other additive's.