I listen to both CD and Vinyl on quality equipment. I've always had a preference for vinyl, and as I acquired both better CD players and turntables/tonearms/cartridges, the difference between them became even more apparent. Trying to describe the difference is difficult, but I would say vinyl sounds somehow more "organic". More of a sense of real musicians, especially on acoustic instruments.
We aren't talking night and day differences here. Casual listening might not produce much difference at all. I'm talking about when you dim the lights and kick back and just let the music sink in. Vinyl just brings me a little closer to the music.
This all assumes the record is a good pressing and in good condition. :)