According to the high-end HiFiHi-Fi connoisseurs' bibles, for a perfect reproduction of the sound, in addition to "special cables", etc., you must have a specialized stage of CD which reads the optical disc and outputs the digital signal.
Assuming that the disc is read flawlessly, the signals should be identical.
If there are errors, the error correction algorithm is still the same as long the number of errors is within the capacity of the error correction algorithm. Beyond this, any "fix" is simply noise.
As I know, and I may be wrong, a very small number of companies effectively produce the CD players' mechanical and optical units, and therefore at least these parts are common to both the cheap and the costly units.
So what makes the difference?