I tend to only enjoy music with most or all of the following attributes.
In no particular order: very high levels of musicianship, musical complexity, deep and broad range of emotional content (expressed musically), (usually) long form songs/pieces, music that can "take me on a journey", so to speak.
Aspects that are unimportant to me: catchy melodies, hooks, verse>chorus>bridge song format.
While not exclusively, I also tend to like music that I may not immediately "get" or appreciate. Music that may require a bit of "work", so to speak.
And it’s not as if I consciously decided to only enjoy music with those criteria listed, but I just noticed over the years, that music that did not have most of all of them, started to bore me, and I found those recordings going unplayed.
I have been in a constant search for music that does fulfill those criteria, and lucky for me, it is very prevalent 
The genres/subgenres that most often fulfill those criteria are:
Prog - avant-prog, symph-prog, Zeuhl, Canterbury, prog-metal, chamber-prog.
Contemporary classical - atonal, serial, Spectralism, avant-garde, New Complexity.
Jazz - fusion, post bop, avant-garde, chamber-jazz, M-Base, "spiritual" jazz.