Digital and analog servos have very similar construction and components. They both use the same type of motors, gears, cases, and have a potentiometer. A digital servo is different in the way it processes the incoming signal and converts that signal into servo movement.
An analog servo when it receives a command to move, takes that signal and sends pulses to the servo motor at about 50 cycles per second, which in turn moves the motor to its required position determined by the potentiometer.
A digital servo has a micro-processor that receives the signal and then adjusts the pulse length and amount of power to the servo motor to achieve optimum servo performance and precision. A digital servo sends these pulses to the motor at a much higher frequency which is around 300 cycles per second. This helps eliminate deadband, provides a faster response to the servo motor, smoother motor movement, and has higher resolution and holding power than an analog servo.
There are some disadvantages to digital servos, but the disadvantages are not in any way close to out weighing the advantages. A digital servo will have a higher power consumption (Around 10 to 15 mAh per servo at idle) than an analog servo due to its higher pulse frequency, so larger capacity battery packs are recommended. Digital servos also are more expensive than analog servos which can get very costly in applications that require many servos.