You are correct in stating avgas is a higher-quality fuel. However, higher octane gas does not have more power. The higher octane number means the fuel charge burns slower and thus is less prone to detonation (pre-ignition). Gas with lower octane ratings burns faster (the mixture ignites more readily AND the flame front advances faster).

People run higher octane gas in cars having high compression ratios to minimize detonation. An example would be race cars, or turbocharged cars when the boost is increased.

Model engines have relatively low compression ratios. Running avgas won't give you an increase in power, but you CAN run a slightly leaner setting without detonating. However this can lead to higher cylinder temperatures, and this is the reason manufacturers don't recommend using high-octane gas. Make sure you have plenty of airflow for cooling!

Brett