Both young Princes were initially commission into the Blues and Royals, The Household Cavalry Division. The Duke of Cambridge chose the RAF as his career service.
During the Trooping of the Colour, his wedding etc he traditionally wear the Uniform of the unit he holds highest rank. He is Colonel of the Irish Gurads so wears that uniform however, I believe that if you look at his uniform he only wear the rank insignia commensurate with his substantive serving rank ie Captain ( could be wrong about this but remembering Staff College thats the rules)