Digital potentiometers versus mechanical?

The best "pots" are actually stepped attenuators: a ladder network of fixed resistors selected by a multiposition switch. A digital attenuator can be mechanized with the same ladder network of resistors, but with the switch contacts replaced by digitally controlled circuitry. Note that in this mechanization the attenuation is entirely analog, and ought to be just as good as the best attenuators.

Eldartford is right about stepped attenuators, built up from discrete parts. There are no digital volume controls, by contrast, that work properly at all (they all loose serious resolution as they are turned down- IMO, a failed concept).

It is possible to build a digitally *controlled* analog volume control, using two different methods, that will work. The first is to use the digital electronics to operate a motor, which drives a regular attenuator, such as is seen in the Ayre preamp.

The other way is to use digital control to operate a relay operated (note- *not* solid state relay) ladder array. A version of this is seen in the MSB digital gear.

Solid state relays can be substituted for the mecahnical relays in the above example but they sound bad.
Both approaches can work equally well if properly executed. But for the purpose of your question, obviously both means are still analog controls.