It's a mixture. Right now I'm listening to Eva Cassidy while surfing. I may have to stop in a few and listen more closely as she's sounding heavenly. However, I think it's valuable to do both with music I'm familiar with. With music I'm not familiar with my first few listening sessions are normally more intent.
I have a system that serves many purposes. First, it's a good system so I can listen critically. Second, my wife is listening now and so this is something we can do as a family. Third, I enjoy something going in the background while I'm surfing. I tend to think better in noisey environments (had no choice in my previous employ, so now it's part of me ...). Fourth, sometimes I just like a good glass of wine and listen for the pure enjoyment of it. It's relaxing.