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Finite control set model predictive control (FCS-MPC) is considered as a new control technique in the power electronics fields which dont require modulation stage. The absence of modulation stage results in operating under variable switching frequency which can affect the harmonic distortion of the output signal, the switching losses, filters design, and so on. On the other hand, the linear controllers control the power converters with constant switching frequency by using modulators. In this paper, the overall performance of FCS-MPC is assessed by performing a comparative study with a linear controller based on scalar pulse width modulation (PWM). The control systems are applied on an autonomous 4-Leg voltage source inverter (VSI) with LC filter as part of an autonomous power supply system. The main purpose of the two control techniques is to control 4-Leg VSI to provide balanced load voltage with lower total harmonic distortion. The steady state performance of the two control techniques is tested under balanced, unbalanced, linear and nonlinear load conditions. Moreover, the effect of the load variations on the switching frequency of the FCS-MPC is discussed. Finally, the performances of the two control methods in tracking the reference voltage under transient conditions are analyzed.