Simply, you can run higher compression ratio while retaining optimum spark advance, and thus get more power.
You can do a long involved study with various manipulations of the 3 variables of octane rateing, CR and spark advance, but I expect that you will come up with about 9:1 for 91 octane and about 8.5:1 for 85 octane, with both likeing about the manufacturers spec for spark advance
Higher Octane fuels means better knock reistance. But an engine having a fixed compression ratio works well using octane 85.5, then it is not required to go for octane 91. Since increase in octane number will raise the fuel cost also.
