What Sonically is the Difference between a $1,500 CD Player and a $10K-$25K One?

A good signal processing engineer, if they are truthful, will tell you that all decent modern CD players have little difference in measured signal output characteristics. Modern analysis gear can measure things you could never hear. However, things like dynamic range and other characteristics do vary. I doubt very seriously there is any significant audible difference between $1500 and $25000 players. Build quality, looks, etc, sure. I work in defense and we use A/D -D/A converters, quality amps, etc, all the time. Modern devices are cheap and perform extremely well. I suspect the truth is (and I’ll get flame sprayed) you are paying a huge markup and the cost of low production quantity components, rather than greatly elevated sound quality. I don’t profess to have golden ears, but I can hear differences in some gear readily. But when you get to a certain level of quality (meaning not Target level components) there is precious little difference in electronics. I do not include speakers in this since they are both “instruments” and components and can have unique sound qualities.

What's the difference between a $2 cigar and a $10 cigar?

Exactly $8.

Find a dealer with a satisfaction guaranty and compare the units in your own home and in your own system is my conclusion.. Opinions and recommendations will be all over the map.. There are too many variables in systems and environments, not to mention the audio experience is subjective..

Listening in your system and in your home is the only way I know of to find truth for the customer. Forums quickly turn into "makes no difference and you are waisting money" to "makes the world a better place to be, and my unit was a godsend".. Either way you need to hear for yourself..
Magazines, forums and audio shows can help people find interesting gear to evaluate, but other than that, the opinions on most any topic, are so inconsistent to be useless.. You can read 1000s of responses and end up right where you started without a clue, until its in your home and system. Thats just a humble opinion and you know what they say about opinions... In your home, in your system. Trust your ears. The rest is irrelevant.. The BS marketing and, I can hear better than you do, down to the chocolatey sound of a copper wire is all fine, although almost unless when buying audio.. Only way to sort the BS is with your own ears, in a known system and environment like home. Surely people give honest opinions, I'm just saying that a consensus on a subjective subject is not likely to happen.. 

The blithely made responses from roberjerman and others are an illustration of what is wrong with chat rooms - often no context for the comments, evidence of limited experience by the writers,  unproductive negativity and often no humble opinion. Julian Hirsch, the famous (some would say infamous) reviewer from Stereo Review magazine back in its day was often quoted as saying there was no difference in the sound between properly functioning amplifiers. He never commented on the so-called quote during his tenure as a reviewer but he was interviewed after he retired and corrected the misunderstanding by saying he had said HE could not hear any difference.
It is absurd to claim there is no difference in the sound from a Sony Discman versus a Theta transport and d to a converter just because YOU can not perceive the difference.
For the record, I have been in the audio industry from fifty years as of this September and have a lot of experience and in my experience I have never heard two CD players that sound identical even if similar in price. Remember, a CD player "makes up" all the sound at its outputs as it sees fit through the complex conversion and filtering process fraught with design pitfalls that are expensive to address in the design. (And there is no music on a CD.) Also for the record I have a rule of thumb that in order to make a categorically better sounding component the price will often be nearly double the price because you can't just make a whiff of a change but need to raise the level of all the subsystems in the component. Thus the price of a better sounding component gets higher rather quickly as you go on an expedition to find "the best." Such is life.

I pretty much stopped reading when I came to, “For the record, I have been in the audio industry from (sic) fifty years as of this September and have a lot of experience and...”

For, the record, I said my Sony Walkman sounded better than a (stock) high end player.