i have just spent three years researching, designing and prototyping remote control intended for volume production. My thesis was that it could nto only be a VERy attractive feature, but superior sonically.
The real answer is "it entirely depends on how".
Leet's take the simplest method- a stepper motor, connected to the existing volume knob's shaft. This will have zero impact - it mimics your hand. So that one is 'sounds the same.
Next let's look at the traditional digital solution (e.g.: what's in your phone, mac, pc, etc). This does binary multiplication on the digital stream. Since there is truncation within the allotted 16 (or whatever) bits and no additional resolution int he DAC, this always degrades the sound. In fact at low levels the resolution falls to about 11 bits. On the other hand the channels track perfectly and there is no additional noise,, aside from the quantization noise (which i note to keep the trolls at bay).
Next we can use a "digital potentiometer" .This is a terrible name, since they are analog and generally dual-resistor pair arrays. Which is very good. But there are technical problems i wont delve into since they are very complex. I made tow sound really good (better than an ALPS or Nobel POT) but only at huge complexity.
Finally you can use a small embedded computer/contorller, lots of relays or analog switches, and pairs of resistors. This is the old Mil-spec method and basically the best there is. Old version used stepped knobs and cost the moon, both in parts and labor. They were also very clunky in many ways. But with a computer, it an be really elegant. That is what i settled on. It makes old fashioned high end POTS sound veiled and shows thier awful tracking. Beware there is no going back, take a deep hit and I've got oyu :-)
So the differences are very much n the details adn about 0.01% here will even understand them. i admit i didn't fully realize what i was getting into with the potentiometer chips - such promise, and such issues.
The best solutions however are not cheap in either engineering or parts,
G