The paper describes the advantages due to the adoption of multi-speed transmission systems within fully electric vehicles. In particular, the article compares a conventional single-speed transmission layout, a 2-speed layout based on a novel gearbox architecture capable of seamless gearshifts, and a Continuously Variable Transmission layout. The selection of the optimal gear ratios for the 2-speed system has been based on an optimization procedure, taking into account the efficiency characteristics of the components of the whole vehicle powertrain. The control system for the Continuously Variable Transmission system has been designed with the aim of maximizing the efficiency of the operating points of the electric motor. The results show that there is a significant advantage in adopting a 2-speed transmission system over the single-speed layout, and, despite a reduction in motor losses, the typically lower efficiency characteristics of Continuously Variable Transmissions do not result in lower energy consumption for the four case study vehicles.