The voltage source inverter (VSI) of an uninterruptible power supply (UPS) is a system where the main objective is to obtain a high quality output sinusoidal voltage with independence on the output load. For this reason, it includes an output LC filter. The presence of the filter increases the complexity of the controller design thus it is necessary to evaluate the performance of the control strategy in terms of the output voltage quality and computational cost of the algorithm. In this paper, both analysis are developed for the finite states model predictive control (FS-MPC) of a VSI performed in the abc and α-β frames. Both algorithms are summarized and compared in order to establish an objective criteria to choose among them when a hardware implementation is developed. Simulation results are presented for both algorithms to validate the analysis.