Typically, there would be no advantage and it would cost more. However, with a higher mileage car, if you are experiencing detonation or "knocking and pinging" it can help. Carbon build up can cause pre-ignition and/or detonation which can be controlled by a higher octane fuel. But you would need to take steps, by utilizing fuel additives and high quality fuels, to reduce the buildup.
The thinking that a higher octane fuel creates more power is mostly false. It can, under the right engine conditions, make more power but generally speaking, octane is just the fuel's ability to control detonation "knocking and pinging".
I have 200,000+ miles on my truck and it can live a long and healthy life with 87 octane (regular) as recommended by the manufacturer, under normal conditions. However, with it's high mileage, the hot Texas summers and pulling my boat, I need to use 89 octane (mid-grade) in the summer, in order to control the detonation.