I know BamaChips did dyno runs with a stock 2011 V6 running 87 and 93 octane.
They saw a 5hp gain using the 93 over the 87.
Members on here state they notice a little better throttle response with premium over 87.
These 3.7s have very sensitive knock sensors and will pull a timing at the slightest noise. That may be why there are gains with 91/93 over 87.
1990 Lincoln Mark VII 5.0 HO 5-Speed Swap- BBK O/R H, Hooker Max Flows dumped, coil conversion
2012 Fiesta S 1.6 5-Speed- 40mpg
Past: 89 Hatch, 89 Notch, 01 V6