If your vehicle is running correctly (no Check Engine Light) chances are you won't be able to tell the difference between 87 and 91. If you use less than 87 octane, the CEL will usually come on especially when towing or in hilly terrain and you will lose some performance.
EDIT: On the other hand, under some conditions, if you work the engine very hard and it gets hot, using higher octane fuel may help restore lost power if due to pre-ignition/detonation. It generally won't INCREASE power, only restore what should have been there. As your engine ages, carbon builds up on the piston crowns and cylinder heads causing the compression to increase. This can cause pre-ignition/detonation. Usually it gets offset by engine wear. Mostly leakage (compression) past the piston rings. As others have said, electronic spark control usually controls everything behind the scene, but not always.
Chum lee