The first thing that comes to mind is originality. I’m interested in pieces that give the sense that the composer has created his or her own individual sound-world. This is more important to me than the style, or “school” of composition.
As for the musical materials: what is it that makes some pitches and rhythms particularly interesting? I can’t define it. And why do some pieces turn out to be greater than the sum of their parts: unexceptional materials that somehow add up to a magical or expressive whole? This is also a mystery.
I play through a new piece and sometimes have an instinct that this is stuff I’d enjoy spending a lot of time with. Also, I’m looking for a piece I might have something to offer, a piece I’d hope to make my own.