I wouldn't bank on anything without actually tracking FE. However, in as simple terms as I can muster:
Typically, if your motor can run with more advanced timing by using higher octane fuel, it will produce more mechanical torque from more complete combustion.
In more technical terms, it boils down to piston dwell time and how long the flame is given to fully burn. So while higher octane fuel does not specifically have any more energy per volume than lower octane, it provides slower burning and lower peak cylinder pressure at the same timing setting, allowing for advancement of the timing to lengthen the burn time, resulting in more complete burning of the fuel and greater torque.
It has been settled. I am filling up with premium... I mean high octane... tomorrow morning. Oh, and I am doing it on my company's tab!!! Haha, hope they like my $70 oil changes and premium fuel fill-ups! Course with me about doubling my colleagues in FE, I would guess that I am still saving them money.