The lower the octane, the easier it is for a fuel to burn.
Putting 116 octane where 87 is needed cuases the engine to run terrible. As high octane fuel requires a lot of timing to burn.
If the question is which "can" make more power.. the 116 wins. Vs which makes more power the 87 wins.
There are a lot of things to look at besides the octane of a fuel. Its possible to have a fast burn rate and high octane. Most on this board are so far off on their tune they are just better off using the highest octane they can get to avoid detonation. I read at least on thread a week where the underlying problem was too little octane and or poor tune. Never seen proof in a thread that too much octane hurt performance. Its possible on certain types of engines that are at the limit of their performance due to the restrictions they have like in roundy round racing. Having the highest BTU possible and not having detonation will be an advantage since BSFC will be less. They dont allow a lot of oxygenation either. Whenever someone asks me how much octane i tell them as much as possible. If they had to ask that question then they are no where near skilled enough to even try running an engine on the edge. Not worth scrimping on octane.