The fixed displacement compressor is a "bang-bang" system, that is, just like a thermostat which only acts on the system's operating status and not also upon its cooling or heating capacity, it's designed to maintain a certain system's property (in that case, the evaporator's temperature) in a certain state (a certain temperature value, or a certain suction pressure value which, for a known refrigerant, matches to a certain evaporator's temperature). It's constantly working to bring the system's property to a precise value. Why? Because, to avoid damage to the system due to too much switching in a too short span of time, the system must feature a certain hysteresis, that is, the value the system should actually resume working at after being stopped due to reaching the desired value, has to be far enough from the desired value that a sufficient time can pass before the system resumes working.
From this standpoint, considering that a warmer evaporator implies an higher suction pressure and therefore an higher discharge pressure (which equates to more work required to the engine to compress the refrigerant vapour), fixed displacement compressors are less efficient than variable displacement compressors (and, to some extent, even other types of compressors, such as the V piston compressor, can be considered variable displacement if equipped with a capacity control system, also known as an unloader, which basically temporarily makes a bank of cylinders useless, i.e. not pumping any refrigerant at all, in some way; capacity control isn't necessarily limited to automotive swash plate or wobble plate compressors).
The latter take the evaporator's temperature in consideration too, instead of just mindlessly pumping any refrigerant they can until the evaporator is cold enough (or the desired vent temperature, if the system is equipped with a thermostat for regulating the vent temperature, is achieved). So the suction and discharge pressures are always steady and at the needed value, not constantly jumping up and down. Hence, once the evaporator's thermal load is stabilized, the engine load is always the same. All of this also thanks to how a thermal expansion valve works by trying its best to keep the refrigerant vapour's superheat steady.
Therefore, they're constantly working to keep the evaporator's temperature at a certain value, rather than bring it to that value.
Externally controlled variable displacement compressors take a step further from internally controlled ones: with externally controlled compressors, the climate control system can adjust the compressor's capacity, and therefore the evaporator's temperature, as needed and in any moment. The latter ones would instead need to be cycled off just like fixed displacement compressors would once the required vent temperature is reached, or the evaporator's air should be heated up again as needed, and both things mean more energy wasted.