If I switch to higher octane , better gas mileage or worse? and why?

Daniel and Country Boy are correct, You can get better fuel economy if you have a vehicle that has computer controlled ignition timing! (this depends on the type of vehicle) How This happens is the PCM "Listens for Detonation from the knock sensor and (retards the ignition timing=less power,less fuel economy) when the octane rating is increased the PCM will keep (advancing the ignition timing=more power,more fuel economy) It's that simple!