I try to use the emotional connection a system provides as my key indicator. The problem is that is a very subjective measure. Yes you can play tracks that have in the past.....err......grabbed you emotionally, but I find this 'measure' is impossible to quantify and is greatly influenced by your mood and concentration levels at the time of listening and even by recent events in your life. So a rather unreliable and unquantifiable measure.
The intelligibility of lyrics I have used as a useful measure and it is certainly more objective and....err.....measurable, but it only gives a view of the accuracy and transparency of the midband. And, there you go, I am already into the rhetoric used by many to judge a system's performance in HiFi terms, as opposed to how well the music connects and engages with the listener. Instrumental separation too is a good indicator but offers little in the musical connection department.
So there we have it. For me the only valuable measures of a system's performance are those that are the most elusive, subjective and impossible to quantify. I am not being very helpful, am I?
Edit: As I posted this I am listening to Bentley Caldwell 'This Love (Is War)' off his wonderful 'The Place That I Call Home' album and I actually welled up, and this track has never connected with me in this way in the past. The recoding quality of this album is not exceptional either. My rig must be doing its thing tonight!