Torque is more immediate and performance better across the band with higher octane fuels,dependent on turbo design and its lag.
(3 octane is not for top end wot performance but allows increased timing advance and torque from bottom to top of the throttle.
Only problem is the cost of 93 octane or 87 octane and octane booster.
There is no gain in power without increase fuel. Unless we get into Adiabatic engines with or without turbos and much higher temps and effeciency, at greatly increased cost, of course.Burnign lots fo lower octane fuel leads to detonation. The engine software ******* the timing and opens the bypass valve sooner,so it doesn't detonate but operates at less power. If you have enough power to get you up the hill fine, but it will use more fuel than higher octane and may still overheat. Heavy enough and it will still detonate.Savings using 87 octane over 93 octane current prices, I have no idea. I'm sure the mfg has tables but perhaps not published.