What are a compound DC motor’s advantages? Speed Variation or Torque?

There are two primary advantages to DC motors: Speed Variation and Torque.

Speed Variation

Speed variation is accomplished by changing either the armature voltage or field voltage, or a combination of both. For example, a motor with a base speed of 1750 RPM and armature voltage of 500 VDC will run at 875 RPM with a 50% reduction in armature voltage (to 250 VDC).

Torque

The definition of an electric motor is a device that converts electrical energy into mechanical energy. In reality, a motor could be better defined as a "torque generator". Torque can be defined as a turning force that tends to produce rotation on a shaft. The primary advantage of the DC motor is that it can develop constant torque over a wide speed application.
Power supply is an important consideration in the application of DC motors. The most common way to provide DC voltage to a motor from an AC line is through the use of an electronic drive. Depending on the construction, the drive will provide a pulse wave form similar to the perfect voltage from a battery. These pulses are characterized by a form factor that is defined by NEMA (National Electrical Manufacturers' Association) as a power supply code. Codes are based on the quality of the power output. Application concerns include drive cost, operational cost (efficiency), reliability, and output power quality.