It depends a lot on the engine. Compression ratio, turbo or not. Most vehicles will make a small amount more power with Premium. If it is designed for Premium, it can make a noticeable difference. The only vehicle I've ever owned that cared, is my 2014 Cruze Eco MT with the 1.4 turbo motor. It calls for 87 octane, but in the summer it runs horrible on 87 octane. I can tell it runs the best on premium unless the temp's are below freezing. I run 93 octane most of the year, 89 octane in the late fall and early spring and 87 octane when the temps are below freezing. I can see how the 3.5 in the Fords with the turbos would behave in a similar fashion. It is only under certain circumstances, but it will really pull the timing and cut the boost to keep from pinging.
In the 6.2L, if you're not towing and in cooler weather, you might be able to get away with 87 octane. If not try 89 octane. If not happy with that under some conditions, run 91-93 octane. You'll just have to try it to see what works. Towing, you probably need premium to avoid issues, but you never know. Weather/temps does make a difference since it reduces the intake air temps and reduces the combustion chamber temps prior to detonation so it reduces the chance or pre-detonation when the temps outside are cooler.
Don't most Hemi's call for 89 octane? At least when towing?
It seems like in years past, it was 10 cents bump from 87 to 89 and then 10 more cents from 89 to 93 octane. Now days it is pretty much a 30 cent bump pre grade. 93 octane is pretty expensive.