1) Transparent tweeter - Feels like a breath of fresh air after being inside a conjested room to hear transparency.
2) The right amount of tension in the woofer - the spring. If you get it just right, the sound becomes round and 3 dimensional - sounds like a ball bouncing. Hard to explain, but every piano student heard that remark before - make the notes round and focused. Sonus faber, and Tannoy got it right for me.
3) Decay - gives a luxurius feel.
4) Harmonically rich and detailed - love to catch all the subtle nuances of a beautiful voice.
5) 3 inch mid ! The best size for a clear mid. Very few of the modern speakers have this.
I like small settelites and a sub sound - like klipsch quintets. They capture the pretty female vocal sounds that pierces your heart in the most satisfying way.
Since we like different music, different characteristics are important for others. I listen to many genre, but classical is my main.