I'm so old school I still subscribe to the idea that the signal should remain in the digital realm until it absolutely must be converted to analog, and then only once. Over the years, this has meant my CD players used a digital connection to the receiver. The type of connection has changed, but it's always been digital.
And, when connected in that fashion, sound-wise they're all the same. Some will have better error correction, shock resistance, features like a 5-disk tray or a big jukebox-style storage area, the ability to burn as well as read, etc. But in the end it's still just 1's and 0's. Fancy players don't "polish" the bits. That's not the way it works. That's not the way any of it works.
ALL of my sources connect digitally nowadays, and that's how I like it. It allows me to concentrate my sound quality dollars on the receiver and, most importantly of all, the speakers. As others have mentioned, I don't even play actual CDs anymore. Any CD I purchase today gets plopped into a (very basic) external CD player connected to my MacBook pro and immediately ripped to FLAC. They're installation media today, nothing more. And I use my receiver's Ethernet connection for music. Anyone who believes CD jitter is a thing (I'm on the fence) should've moved that way years ago, since--as far as I've ever been able to figure out--that connection style does away with jitter completely.
There are (obviously) folks who think they hear differences big or small in every change they make. I'll wager they dedicate a significant portion of their budget to cables and power conditioners. Hell there are people who spend enormous sums on turntables, a technology that dates back to the 19th century.
So, apologies to the departed IntelliVolume, no, when connected digitally there is no sonic difference between a $5k dedicated CD player bought from a boutique shop and a $50 blu-ray player from Wal Mart.