Good question, Charles! I grew up with music constantly flowing - father played piano, me and all siblings played various instruments and while none of us are (or were) professionals, there is definitely something about the sound of live music that engages and excites. I wish I could translate that into audio terms - dynamics, speed of transient response, tuneful base, rich mids? I can't say exactly, but I know when I hear it.
Now, when I really started exploring the whole audiophile thing, I did get caught up in detail, imaging, etc... but then questioned where that was taking me. Yes, live music generally possesses those characteristics (at least from the right seats), but I know that when I'm listening to live music, I am so not paying attention to that, but rather just getting lost in the music. And, as with recorded music, a poor performance can be just as unfullfilling as a bad recording or a poorly setup audio system.
I'd be very curious as to how people listen to live music versus their audio system...