Interesting question and my experience
I have been playing my CDs mostly on my Pioneer Elite 47A DVD player. (Its a universal player that plays SACDs and DVD audios as well). I use digital out for CDs. I recently decided to audition a Rotel RCD 975, a fine CD player by the numerous reviews I have read, with an outstanding set of Digital to Audio Converters. I brought home a used one from a local hi fi dealer and plugged it in using a good quality connect (yeah Monster Cables, but it was either that or Radio shacks own brand, and even though overpriced, they do make a good interconnect). Well I put my Yamaha Receiver on Direct Source no effects, so the sounds on my Pioneer DVD player and Rotel CD player went straight through the Yamaha and into a Rotel 200 watt per channel power amp and into a pair of Polk Monitor 70s. The Pioneer used a digital connection, the Rotel I used the Analog connects, since it has outstanding DACS. I put in a copy of Donald Fagen's latest CD, Morph the Cat into each player. I had two because after I bought the CD, I found out he had also released the album in a 2 pack with CD and DVD audio. Well I listened, had my girlfriend switch back and forth between the CD player and the DVD player. Guess what? I could discern no difference whatsoever. I really couldn't, and I tried. They both sounded beautiful, full bass, great vocals, nice saxaphone, good imaging. However, I couldnt tell the difference between the Rotel and the Pioneer. I give big kudos to Rotel for having analog outs that sound the same as the digital out on the Pioneer, but bottom line, I couldn't hear the difference. For reference, I can certainly hear the difference between SACD and Cd, CD and Mp3, using good connects vs. the first pair of cheap RCA cables I could find in my closet. (hence the trip to radio shack for the monster connects). I could NOT note any difference between a state of the art Rotel and the Pioneer DVD player. Perhaps when one goes above the $750 mark (the original retail price of the Rotel) into more esoteric makes the difference is clear, but for what it's worth, that is my experience. Hope it helps!