What I am referring to in the case of "music" is the chords and structure of the song. How complicated should the chords be? Should you stick to more basic chords (major, minor) or start adding extensions? This can also pertain to the time signature, feel of the song, etc. There are lots of variables here.
Bands such as Dream Theater I feel look at the musicianship of what they do as the main priority. In pop music, really the melody is king ala Katy Perry, Green Day, Maroon 5, etc. Then you have artists like Bob Dylan and more of the singer/songwriter/folk type whom aren't the most melodious or musically complex, yet have amazing lyrics and ideas. That's not to say any of these bands or artists don't possess all three characteristics.