not all CD players sound the same
I have several different machines on which I've compared CD quality. I use a headphone amp and a pair of Sennheiser HD650 headphones that I can move rapidly from one machine to the next, and the differences between all 3 of my machines are obvious on CD's. I have a Sony SACD/DVD player DVPNS755V, which I think sold for less than $200. Compared with the Denon 3910 universal player, the Sony produces CD sound with much less impact and clarity. You can almost feel the bow bite into the cellos in a classical symphony CD on the Denon, but on the Sony you just hear a slightly accented attack. I also have a Marantz CD-67 SE-II CD player, probably a decade old, with an original list price of, I'm guessing, $400-$450. It sounds nearly as good as the Denon; the sound is a bit warmer, probably more than it should. Among these three machines, it would be the one I'd use for some of the early and edgy digital recordings.
I haven't heard the Cambridge or Rotel units you mentioned, but I am absolutely persuaded that there are audible differences in quality among CD players.