This paper presents a comparative study of three Predictive Current Control (PCC) schemes for Permanent Magnet Synchronous Machines (PMSM) drives. The first control scheme predicts the future evolution of the currents for each possible configuration of the inverter legs. Then the switching state which minimizes a given cost function is selected and applied during the next sampling time. The second control scheme uses a modulator to apply two configurations of the inverter legs during a computation period. Among these configurations, one leads to null voltages. The duration of the other configuration is calculated in order to minimize the distance between the obtained state vector and the desired one. The third control scheme uses a model of the PMSM in order to predict the stator voltages which allows to reach the desired currents after one modulation period. An algebraic method is presented to compute the duty cycle of each leg of the inverter in a direct manner. These control schemes are detailed and tested using the same switching frequency on the same test-bench (1.6kW PMSM drive). A simulation study is performed in order to compare sensitivity to parameters of each control schemes. Experiments confirm the simulation results.