Recently, the control of multiphase electric drives has been a hot research topic due to the advantages of multiphase machines, namely the reduced phase ratings, improved fault tolerance and lesser torque harmonics. Finite control set model predictive control (FCS-MPC) is one of the most promising high performance control strategies due to its good dynamic behaviour and flexibility in the definition of control objectives. Although several FCS-MPC strategies have already been proposed for multiphase drives, a comparative study that assembles all these strategies in a single reference is still missing. Hence, this paper aims to provide an overview and a critical comparison of all available FCS-MPC techniques for electric drives based on six-phase machines, focusing mainly on predictive current control (PCC) and predictive torque control (PTC) strategies. The performance of an asymmetrical six-phase permanent magnet synchronous machine is compared side-by-side for a total of thirteen PCC and five PTC strategies, with the aid of simulation and experimental results. Finally, in order to determine the best and the worst performing control strategies, each strategy is evaluated according to distinct features, such as ease of implementation, minimization of current harmonics, tuning requirements, computational burden, among others.