Headphone listening has made me a better listener, but I was an 'audiophile' before I ever wandered into the headphone aspect of the hobby. So I had already cycled through the traditional 'moves' in terms of acquiring a lot of 'better recorded' music and expanding my musical interests (i.e., discovering jazz and blues, etc).
But I do think headphones bring you 'closer' to the music in terms of details that you can hear that you might miss with speaker rigs. Thus, you tend to become much more interested in music that is on the complicated, textured, intricate and diverse side of the fence. It becomes more difficult to listen to standard fare 'pop' and 'rock' music (although there are obviously exceptions) but headphones are perfect for most jazz and blues, as well as ambient/house types of material.
I (for one) am not a terribly big fan of (most) classical music through headphones. For my tastes, I need to hear an orchestra while sitting in front of my speaker rig where I can get a better sense of placement and depth perception. It seems that I miss a lot of the beauty of what classical music has to offer with headphones.
For a totally different reason, I don't like much 'classic rock' through headphones, but it's not what I'm "missing" so much as it is that annoyance factor of getting an all left or all right signal far too often. The amps I use don't have crossfeed, and I think this is needed with much of the poorly recorded music from the 60s, 70s and 80s.
