All I've seen is that everyone says rosemary is better, including the Perfect Hair Health youtube channel IIRC. With peppermint, there were some studies done on mice that showed regrowth, but no studies on humans that I'm aware of. Rosemary was studied on humans and shown to be as effective as minoxidil.
I do think peppermint is beneficial. It's antifungal/antibacterial and increases blood flow. It's in the Dr Bronners castille soap I use as shampoo, so I get rosemary and peppermint. Both bases covered.