higher octane pump gasoline only has a higher flash point. it can withstand higher heat/pressure without detonating.
it does not have any more thermal energy within it.
if you advance your timing you may see a little power increase and little better mpg.
but if your engine has a carb on it and you just put in premium, you will make less power.
91 will burn colder, releasing less heat/energy when used in an application where 87 can be used.
newer engines with computer controls where things may adjust due to less knock or something, then yes you may notice a difference.
high actane gas in a low compression application is more likely to have deposits and unburned hydrocarbons left behind like on valves and introduced to the oil which creates acid.
similar effects as running too low of coolant temp along with low compression.