Well, this is maybe a bit of a tangent, but I know there are many musicians, even those who are interested in jazz music, who despise the sound of the Hammond organ in that idiom.
However that may be, I consider it a good example of how recording the speaker (whether it's a Leslie speaker or a Hammond "tone cabinet") can be perceived differently IRL than in the recorded form (properly mic'ed, of course).
I've had long "arguments" with live sound technicians about how much of the live experience can be reproduced, and first captured, and particularly with the piano.
My own conclusion is that unless one is prepared to invest n amount of money into very capable speakers and drivers, it's not a question.
OTOH, I only know a small bit about live sound: on a recording, take, the generally superb solo piano records at Maybeck Hall...I'd just guess that it sounds better reproducing the sound on my crummy, ancient Altec 15 and a generic power amp and preamp at home than sitting in the audience and listening to people unwrap their cougdrops and all that.