One of them has to do with distortion. Digital Distortion and Analog Distortion sound different because of two basic factors. When tubes in amps distort you get harmonics that are more pleasing to the ear, and tubes gradually distort wherein digital signal has whats called a "hard knee" it is clean until that level is reached then it distorts quickly.
The other reason Analog sounds better is because of info captured during the recording process. Analog captures whatever the mic is capable of capturing as long as the analog recorder can lay down that signal to the physical media. Digital captures only part of what the mic gets BUT that is because of the limiting factor of how the digital recorder is constructed. Digital Media is fast becoming capable of holding the same amount of information analog media holds and as we get farther along in digital recorder equipment design that factor of limitation is becoming less of a problem.
The bottom line is digital takes a messy analog signal and makes it sterile and the pleasing part of a recording resides in that messy part that digital cleans up. But as technology advances, digital is becoming more and more capable of recreating that messy part we love to hear.
Natural sound is a Gift from God, and yes, many a Master leant an ear and mind to the study of it.
Pachabell’s Canon in D is simplistic if you to not hear this.
Truly, with the sample rates we have now in Digital it is getting better.
Sadly, now my ears are shot. LOL
Bob Carver, the legendary amp designer was one of the first to get “tube sound” from transistorized components by means of shaping circuits. Others have done similar work in digital to analog circuits, if one wants to pay dearly for the high end audio stuff. I dearly love Yamaha’s amps and receivers (even their low end stuff) for their utterly clean sound, even with the DSP being used to create their legendary digital sound fields(from digitally sampled echo info taken from famous public and concert venues).