I think I go for a sound that's in my head. However, that sound is very dependent on what style of music i'm playing and based on what I've heard others do in that genre. To answer your question, I suppose that means I do a bit of both!
Putting it another way, I can' t think I have ever sat down with my rig and tried to get a tone like player X but I do make genre specific choices to achieve my desired tone. For example, I swopped my Spirocore Weichs for Golden Slaps when I joined my current blues/swing band to get a sound more authentic to that style of music. Recently, I played with a punky pop band and realised some fuzzy bass would sound great. I wound up the front end of the Streamliner, put the Sadowsky on the front pick up and everyone loved it. I've never used a sound like that before but it was the one in my head for that set of songs. Did I get that from hearing someone else? Quite possibly.