WOW. There is no real short answer to this and I am not known for short answers.
I have a lot of experience with hi quality audio having worked in hi end audio shops since the '70’s and in large room sound reinforcement. Sorry to say it was my constant exposure to high sound pressure levels for long periods for many years that is a major reason I can no longer enjoy that interest due to my hearing loss. But you don’t forget what you learned.
The debate of digital vs analog has been going on since digital hit the audio and recording industry. At first it was thought it was going to be the end to all problems but little did they know that it would usher in it’s own problems.
Generally speaking, digital has more of a harsh and processed sound. Grammy award winning recording engineers have expressed this. Digital audio is literally small bites or samples of the analog wave taken one bite at a time like a snap shot or picture. The more bites or samples a second, the smoother the sound. I would be interested in seeing the sample rate for my HAs
Natural sound is analog as it moves through the air. It is not a simple pure tone sine wave. Sound as we hear it, especially music is a complex wave. If you saw it displayed on a scope you would see what I am talking about. Sound produces a complex wave of over tones and harmonics that result from the combining of different frequencies and tones. For example, in a simple example when two tones at different frequencies go through a system, you will not get out just the two tones that went in, you will get four tones out. You will get a tone that is the sum of the two, (a 60 hz tone and a 80 hz tone will sum to 140 Hz) you will also get a tone that is the differance, (80 minus 60 is 20). The 140 Hz and 20 Hz tones are called harmonics. So just consider all the harmonics you have in music. That makes this sampling and processing all the more complex. It has to go through a analog/digital converter for the processing then a digital/analog converter to be used by the speaker to make sound waves that your ear hears.
To try to sum this up, you have to consider what you are dealing with. Your digital HAs are small and often offer multiple channels of compression and feed back supression. The circuitry that does this just can not compare with that used in audio recording studios and hi end sound reinforcement systems and yet even those in the industry will say that they can tell the differance between an analog recording and a digital one.
Over the years, oddly enough, it has been the general opinion that digital recording and sound reproduction works better for classical and orchestral type music and rock works better in analog. In a recording industry trade magazine I subscribe to, one engineer actually was going to record a few tracks of a song in analog and the rest in digital because of the instruments involved.
Sorry for taking so much time to offer my 2 cents worth on this but to expect such a natural sound from digital devices that are so limited in what is capable in such a small package is unrealistic. Digital precessing equipment in sound systems and recording studios literally take up racks of equipment space and take considerable training and experience to operate properly.