TTN, as Commandant is a post not a rank I think they made Harry a Commandant as he does not have sufficient seniority to be a Commodore. When it was first introduced there were enough senior Royals.
However I see he is a Naval Commodore. Edward is a Colonel and also a Commodore at Waddington, so I am not sure.
The link is a fascinating summary of military service. I wonder why Andrew has so few medals compared with his younger brother.
https://en.m.wikipedia.org/wiki/Military_service_by_British_royalty