As a hobbiest jazz musician myself, I can tell you that being at a live event is a completely different experience from music played back in the home.
The experience I get standing next to the rhythm section and other horn players and singers is not the same thing as what happens when I turn up my rig. This experience is all about interacting with the other musicians, adding licks or honoring their playing. This is the essence of a good band, IMHO.
If I am playing in a classical sax quartet, we have been trained to play targeting an imaginary point above and just forward of the quartet's position on the stage. This imaginary point is the place where the 4 sax tones mix into one tone. There's no way a recording is going to track this no matter how many channels are used or the placement of the mics; although Prof. Keith Johnson of Reference Recordings seems to have come mighty close.
As for instrument tone accuracy in playback, one of the greatest compliment a musician can give another musician is that their tone is good. As a sax player, this implies that the player has spent many hours focusing on how their horn, reeds, mouthpiece and their playing muscles have been honed and formed. When you read interviews with the greats of any instrument, you'll see them saying what a tone this or that influence has.
One reason, I believe, why many top-end musicians have small stereos for personal playback (there are exceptions like Keith Jarret) is that they are trained and experienced well enough for them to get the cues they need to fill in the missing tonality. Can you tell the difference between a B-Flat #9 and a B-Flat flat-9 chord? Good musicians can identify them with a set of iPod headphones because of their training and experience.
What has this got to do with the difference with a stereo playing back a sonic image of a performance?
Well, I can hear a bit about a player's tone on a recording - enough to identify them by their playing at times - but it doesn't come together until I get to see and hear them live. For instance, one of the best jazz sax players living right now is Phil Woods. His soaring solos are wonders to behold and his tone is impecable - on a record. When I hear him live, I can hear his horn just 'glow'. It does...it just shimmers and the sound seems to come from around it rather than out of the bell. No recording of his playing conveys that aspect nor do I get to see the interactions with his long-time drummer, Bill Goodwin. You have to be there.
Note that I didn't say anything about the PA's effects. None of the above will _ever_ get conveyed with a PA. This is why jazz venues use as little as possible.
Just my perspective......
Cheers,
David