Hysteresis effects hinder the accurate control of electromagnetic actuators and require auxiliary sensors for properly determining the hysteretic system state. The physics-based Jiles-Atherton and the phenomenological Preisach hysteresis models provide powerful means to describe the magnetic hysteresis and its inverse. In this paper, we consider both hysteresis models in the scalar form from the control points of view, with a primary objective of the sensorless inverse feed-forward control. The identification complexity, the runtime, and the space efficiency of the control-oriented implementation are analyzed and compared for both modeling approaches. Their control performance for an inverse hysteresis compensation is experimentally evaluated on a specific force-controlled electromagnet system.