The combustion efficiency depends mainly on two parameters:
-The quality of mixture between gasoline and air,
-The gasoline composition.
If Mixture is not good the efficiency will be low. But the mixture quality depends also on the temperature, the technology of mixture, the pressure, the characteristics of gasoline, etc.
Otto-type engines compress the fuel/air mixture and then ignite it. The higher the pressure that is achieved, the better the efficiency.
The problem is that fuels can self-ignite at high pressures which leads to rough operation, "knocking", higher emissions and reduced efficiency, sometimes even to damage. Since this has to be avoided, the self-ignition characteristics of different fuels have an impact of efficiency, since some fuels can be compressed to higher pressure levels than others without self-ignition.
In gasoline technology, an empirical property called the octane number is used to describe the propensity of a fuel for premature self-ignition. The lower the octane number, the more likely a fuel is to self-ignite.
The RON number is more about anti-knocking abilities, instead of the performance.
In a lot of areas, the gasoline sold by gas station is mostly E10(up to 10% ethanol in the gasoline). Then I would say sometimes the performance difference felt by the driver can be mostly caused by the different percentage of the ethanol (which reduces performance by a small amount).