The CEC TL51XR is in a different ball park soundwise compared to the other players mentioned. The CEC delivers a very analogue, relaxed tonality that belies the standard 'hyper detail' CD sound you might find on traditional players. While the Cambridge and Rega definitely have their strengths in sound smoothness you'll find in one way or another there's usually a compromise. Like bass slam or midrange compression during busy passes, or treble roll off. My dealer that sells Rega, Cambridge and CEC never budges when I ask him what is the better player. He's seen a few 840c's come back for repair too.
I had the Consanance CD 120 and was amazed for the first day or so. Then when my ears started bleeding from the impression that I was hooked up to an audio microscope I sent it back. WAY too clinical. NOT musical. Like it was on steroids and speed. The CEC, I find, strikes one of the most neutral balances between detail (without compromise) and musicality (smoothness, and just a hint of warmth without being 'colored').
I compared it for kicks against a shop owners Pioneer SACD/universal player. He had an SACD disc and I had a redbook CD. He heard information in the bass on the CEC he couldn't hear through the SACD!
A more apparent difference was the Arcam FMJ cd 33 vs the CEC. Both were very close but the Arcam sounded more 'lively' in an exaggerated way. Like an EQ on a processer was turned on. The CEC just plays it like it sees it, so to speak. The Arcam 'wows' you. The CEC humbly presents you the simple truth of the recording. Most revealing was busy passages. The Arcam compressed and became confused in the soundstage. The singer got swallowed up in the melee of sound, while the CEC never broke a sweat, and showed all instruments as if they were solo. The Arcam is nice dont' get me wrong. But if you're an audiophile and seek perfection, the CEC is a step above, and almost $1500 cheaper!!! It's very buttoned up but still offers a warm hug.
Being an owner I've found the player benefits, like all gear, from being pampered a bit. Isolate it! Give it a very nice power cable, and IC's and you'll see where it really shines. I put a Virtual Dynamics Power 3 cable and it opened up wonderfully. I'm using Rollerblocks underneath, then a 2" maple board on brass isolation cones.