It depends on what I am listening to. Some songs are all about lyrics, and others are about the moods created by abstract sounds. Compare:
The whole point of this one is that it tells a story with the lyrics, so when I listen to it, I listen to the lyrics.
When I listen to this, I am not paying attention to the lyrics. I don't have any idea what she is saying, nor do I care. I doubt the lyrics have anything to do with the point of this song.