Are you serious?
First of all, BTU is the absolute most ridiculous unit for measuring a fuel's ability to make powerful combustion.
An engine is not a water heater or a dryer.
This is especially true for turbo motors because exhaust gas pressure/energy contribute directly to the car's power.
Second, how are you both asking a question and making a statement?
Yes, running 91 octane allows you to run more aggressive timing which translates into more power.
Ever been in an older high performance car using a distributor with bad centrifugal weights?
The weights spin outward based on engine speed and advance timing - when the weights are stuck the timing won't advance and the power flattens out early in the RPM band.
The horse has been beaten about the dual-map in the Sonic's ECU.
You fill up the tank the ECU uses 'the good map', an aggressive timing map, until it detects knock then bounces you down to the ****ty map.
You could, in theory, stay in the good map if conditions are great ; maybe cold weather, not going to hard on the throttle from stops/high load but I wouldn't count on it.
I don't mean to sound rough, but this issue is getting a little old especially since the benefits of aggressive timing go back to the beginning of motor vehicles.
If there's ever any question feel free to pop the hood on a vehicle and retard the timing and see how the vehicle performs.