The octane rating is simply the resistance to detonation, think of a diesel engine. You will not see an increase in performance going to a higher octane fuel and may actually see a decrease because of the slower flame propagation due to the higher octane rating causing a slower burn.

The best fuel to use is the lowest octane rating that does not detonate. Just because 87 does not detonate in winter does not mean it won't in the middle of summer when temperatures rise. Of course there are safety margins in BMW's recommendation of 91 under most normal operating conditions but why chance it for a few dollars a tank. I have destroyed several race motors due to detonation and it is not cheap!