What makes a Cd player a Great cd player

It's well designed and built.

That doesn't necessarily mean it has to cost a fortune these days because the basic technology needed to do it well is fairly commonplace and also fairly widely understood these days.

How different units are tuned to sound from there is a different story, more one of personal tastes and how well the player integrates with the rest of the system (amp, speakers, room), which can make a huge difference in regards to the final results

Personally, I would assess the player's and systems results using live music performances as a reference standard, not a different format of recorded media, vinyl or otherwise.

If things are going well, either format will do a good job of getting most things mostly right in their own way.

"There is a problem, as you said, that when going from a good CD Player to a better one, it does have a tendency to bring to light the difference in recordings."

Recordings are what they are. Don't blame the CD player or system for them sounding different. That is the way it should be. If they all sound similar and not all that great to boot then you may have a problem worth addressing.

A good setup/player should bring to light the differences in recordings. Lesser recordings for the most parts should only sound that way because now the better recordings sound better or at least different.

Train yourself to accept what is in the recording rather than trying to make them something they are not. I find that 90%+ of CDs have something good to offer in regards to sound quality. Few do it all right in the same recording, but if you can cover all the bases by listening to a variety of recordings, then you are in very good shape!

As an extreme example, on my music server, a small % of the 10000+ tracks are cuts I digitally recorded off of old 78s playing on an old Admiral ceramic cartridge rim drive table I picked up for $10 at a yardsale for just this purpose. These tracks have some of the most captivating and lively unobstructed midrange there is. That is their strength. There is also a ton of background noise and not much else to brag about, including an unusual overall timbre, but they are what they are (90 year old early recordings that are easily identifiable as such), and are quite enjoyable to listen to as a result.

Wow, didn't realize the DCS DAC architecture could be had for that price! I'd jump on that deal if the Arcam sounds anything like the DCS gear I have heard!

Yes, the ring dac architecture for applying dither from what I have read strikes me as a very practical way to achieve higher resolution yet retain a smooth response and full dynamic range. When I've heard the DCS gear, what my ears heard was consistent with what I would expect having investigated the technology in more detail a bit later after the fact.

That DCS sourced system produced some of the most natural sounding massed orchestral strings I have ever heard from a CD source. I attribute at least part of that to the unique Ring DAC design.