Octane rating has no impact on BTU's. Additives used to increase Octane simply prevent the fuel from detonating early, in higher compression engines. High compression engines will experience pre-detonation (a.k.a. Pinging & knocking) when using regular grade gas. This can cause valve train damage over time.
If your engine is designed for regular gas, mid grade or premium is a simple waste of money. If your engine is designed from premium grade fuel, being a cheapskate is gambling with your car's longevity.
Finally, to complicate matters, many newer cars have the ability to adjust to the grade of gasoline used. These cars can be identified by the term, Premium Grade RECOMMENDED, instead of REQUIRED. Those engines will retard timing a bit when lower grade fuels are detected. They will run fine, but performance MAY be slightly affected as well.....