This article from the sidebar of the Free-Jazz Stef blog explains why I appreciate Jan Garbarek but not Kenny G. I couldn't have said it better.
Here are some criteria which I find very important, and true, there may be overlap between them all, but they still have their specific shades and colours of value, and there may be other criteria to add.
1. Authentic: the emotions have to be real, genuine and truthful, the prime objective should be to create good music for the sake of the music itself (not in order to sell, or to show off, or any other thing …). That's why I like improvised music, because the link between emotion, musician, sound and listener is to be found in its purest form. It's your immediate emotion you're transmitting, not someone else's. Paradoxically enough, this also includes "absence of self", as a prerequisite for true interplay, listening skills and communion between band members.
2. Adventurous: the artist/band should be looking for new ways to express what they feel and have to communicate. What's the point for the listener to hear the same kind of approach as others have tried. The surprise element, the creativity, the musical vision are part of the adventure. As a listener I want to be taken along, and explore new musical horizons.
3. Accurate: when you hear the sounds, you must have a reaction of "Yes, that's it!", as the sublime translation of feelings through skills and mastery of the instrument, the total sound created by a band or the newly created musical language. The sound, or just obtaining that single note which encapsulates it all, yes, then you know you've transmitted something as a musician, that you've received something as a listener, that you share something. Doing that requires accuracy and concentration.
4. Artistic: by that I mean the more cerebral aspect of music. There is some concept behind it, which leads to structure, balance, length, interplay, selection of instruments, of musicians, of new approaches. This does not go against improvisation, quite on the contrary : great improvised music is all about artistic vision, clever group interaction.
5. Attention-Grabbing: though music can and should require an effort from the listener, it should also include a factor of entertainment, in the sense of keeping the attention going, of being captivating. Lots of music, and especially during long soloing, contains the risk of losing the listener somewhere along the way, even if the musicians themselves are very intensively busy with interesting things. There is of course lots of music which does not take the listener into account at all…