OOlufoks, the difference in sound is not just do to the mic, it's all the reverb that's added when you play through a mic into a soundboard, as in PA or recording.
I used to see Richard in the 80s when his solo career was just taking off. He played for free on Sunday afternoons in a bar in Manhattan Beach (LA suburb). My wife and I were there most Sundays since we didn't have a lot of money at the time, and he always had good up and coming musicians in his band. At that time he was playing a Strathon, the plastic mouthpiece with an adjustable baffle. Obviously that's not what he's playing in that video, I just wanted to add onto the mouthpiece history started by Joe Jazz.