An analog console will accept voltages straight from a microphone or direct input box. A digital console will first convert the voltage into digital information.
An analog console allows the user to be “hands on” with each controller affecting a particular parameter. A digital console allows storage (snapshots) of the console's state for easy recall.
An analog console may have dedicated EQ and compression built in, while a digital console can have many different effects included in its software.
No noise is introduced into the signal path when being routed around a digital console. However, the audio must go through an analog-to-digital converter at one end and a digital-to-analog converter at the other, which introduces subjective audio quality loss.
Analog consoles are generally larger, as they have dedicated faders, inputs and EQ for every channel. Digital consoles are able to use one set of controls for many channels.