It is a difficult question, as pointed out by
@Analog Scott , and I would agree with his comment that you probably have crossover between "pleasing" and "natural" (or live) sound.
We don't all have the opportunity to compare a recording of live music performed in our living room with it's playback on our system, as
@morricab did.
To make things as simple as possible, at least for me, I ask myself: what do I want out of my system? Why bother, and not just listen to a cheap stereo? What immediately comes to mind is the ability to dig into the recording to hear all the subtleties, feel the "ambience" of the recording and better capture the unique sound of each musician, with as little coloration as possible. That's when the recording comes alive, at least for me. I get this with good quality headphones. If I could get to the same level with my speakers (with all the benefits speakers bring over headphones) I would be pretty happy.
P.S. the reason we go around in circles with these discussions, I believe, is that live music, often heard from an early age, obviously conditions our listening. Everyone uses "live music" as a reference - we cannot escape that.
But things are not so simple, because every instrument (and voice), every venue, and every microphone is going to be slightly different (not to mention the rest of the process that results in the analog or digital media). So how do we know whether what we hear on a recording sounds tonally accurate, for example? We cannot.
Frequency response gives us clues. But a perfectly linear frequency response comes at the expense of some other sound characteristics, so we have to compromise... There is a reason why we are not all listening to Magico speakers, for example.
Moreover, frequency response curves may not be representative of the behavior of a system's performance when playing actual music as opposed to "noise", and may not capture small deviations that become significant when we listen to music ("continuous" sound from an instrument, with all it's complexity) as opposed to a series of distinct sound bytes.
When we consider other aspects, such as a system's ability to reproduce low level detail, the measurements are probably more complex. Fortunately, it is fairly easy to simply compare various systems, we don't need live music as a reference. Detail is really a function of the recording itself, not of the performance (setting aside recording venue acoustics). Also, in many cases, there is much more low level information to be heard on a well-recorded performance than can be heard in the live venue.
The same could be said of other aspects of sound reproduction, such as "presence" and "dynamic response" which can be felt easily when comparing systems with specific recordings. I am not sure you need a direct comparison with live music.
But all these aspects of sound are also found in live music. So we just go around in circles. Just saying something sounds "live" or "natural" is nice, but it is not enough. For every sound characteristic we appreciate, there are always sacrifices that are made.