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

These kind of questions are sadly just going to do no service to the person who is asking. I am sure you are asking in pure hearted curiosity. Unfortunately you are wading into a battlefield occupied by several armies.
There are certainly many CD players that are over priced but to say that all high priced players are flim flammery is to dismiss the costs of development, testing, parts quality, manufacturing, distribution, etc.
It is a complex question that can really be understood best by auditioning a lot of equipment yourself.
In my case, I have heard a lot of stuff in a lot of different settings to come to my purchasing decisions.
I would just advise setting a budget and listening to as much as you can (Never mind the price) then settling for what you feel hits the mark in your range.
For me, I ended buying something that was about a third more than my original budget because it just sounded worth the money.
You can read all of these posts and get a feel for all the current hardline attitudes and then make your decisions.
My decision has always been to trust my ears. Mostly they haven’t steered me wrong. If they do it is usually because I didn’t listen long enough or carefully enough without distractions.

I had a Bryston BCD-1($2,750) and found it superior to what i had heard before. It's shot and my limited funds have gone into analog playback instead. Though i would trade into the Bryston BCD-3, $3,750, ($2,200) with returned BCD-1. I heard a $15k disc player at a friend's which sounded far superior to the Bryston. Zero shortcomings,  very analog. I don't have a DAC, next time some money shows up I may dive deeper into analog by adding a second tonearm for a mono cartridge and phono stage. Leaving digital out of my listening room.

glupson - Correct that CDs don't fail very often, the laser is usually at fault. 1 or 2 out of 7,000 CDs made since 1984 have failed me. I make it a point to clean the laser every year (1,000 hours) or sooner. It makes a difference with 80+ minute CDs (London classical reissues sometimes go to 85 minutes).  
Elizabeth and roxy54 - I 100% agree.  The mastering is numero uno in the resulting quality of vinyl and CD.  Just last night, I played Turandot/Mehta on a London CD but when the chorus came in, it was a hashy mess.  I put the LP Decca version on and bliss, full, detailed sound.  (Why do so many of my London opera CDs sound like poor quality remastering compared to the LPs whereas London's mono classical sound superior to their LPs)?  
I went through about 40 used CD players from 1985 to 2000 (mostly average quality/$500-$1500 Denon, Sony, Yamaha, Marantz etc.) until I found the EAR Acute 1 in 2007.  Audio nirvana with NOS tubes and cabling.  My friend upgraded his CD only system with a COS Engineering DAC using a Pioneer Elite DV05 as a transport.  Yes, it's got superior resolution.  I do not have the problems geokaitt claims CDs have with well recorded and mastered CDs.  My sound engineered audioroom cost twice as much as my main audio system but it's worth it (only an external tweak here and there, no big change ever again).  I have friends who are CD or vinyl only listeners.  Funny how they both enjoy my quad  front end system (plus RR and 78s).   CDs are just easier to use than LPs.  

Well, couldn't resist dipping my toe in here. 1st let me say my system is modest by audio mag standards, but it sounds good in my room. I have both a decent TT and several hundred albums, and I do love the analog sound. That said, I also have 3 disc players: a Sony EX5400es and an Oppo BDP 95, both modified by ModWright, and a Sony 555es changer, modded by Matt Anker at the now-defunct SACDmods, who was then at OSU but is now in the Navy. I listened to each of these players before and after modding, and I must say the difference is audible. Each was an excellent player out of the box, but the mods take it to a new level. 

I won't bore you with the details of the mods, you can see those on ModWright's site, but a well-recorded redbook CD or SACD on any of these produces delightful results. Different, but all good to my ear. And as between vinyl and CD, yep, I like them both. Different, but good. 

The mods took each of these players from an original cost of around $1500 (a little less for the Oppo) to around $3500. Well worth it IMHO. Would 10X more produce 10X "better" sound? No, because the law of diminishing returns applies in spades where audio is concerned. Better, probably, but possibly not audible. And we must also consider that there are many links in the audio chain, from the plug in the wall to the room. Any weak link in that chain (including and especially the quality of the recording) would make it difficult if not impossible to assess the difference in any one component. And compatibility with your own system is another factor to be considered. 

Anyway, it's a fun hobby, and it stays fun as long as you find something you like and stick with it instead of chasing the elusive absolute sound. Remember it's really all about the music, not the gear. I think I'll go listen to some tunes now. Vinyl or CD, and which player... hmmm, maybe I'll flip a coin.

I didn't bother to read through the posts, but if you have to ask that question, there probably won't be a difference to you, but I suspect that you are just a troll.