This work presents a detailed breakdown of the energy conversion chains from intermittent electricity to a vehicle, considering battery electric vehicles (BEVs) and fuel cell electric vehicles (FCEVs). The traditional well-to-wheel analysis is adapted to a grid to mobility approach by introducing the intermediate steps of useful electricity, energy carrier and on-board storage. Specific attention is given to an effective coupling with renewable electricity sources and associated storage needs. Actual market data show that, compared to FCEVs, BEVs and their infrastructure are twice as efficient in the conversion of renewable electricity to a mobility service. A much larger difference between BEVs and FCEVs is usually reported in the literature. Focusing on recharging events, this work additionally shows that the infrastructure efficiencies of both electric vehicle (EV) types are very close, with 57% from grid to on-board storage for hydrogen refilling stations and 66% for fast chargers coupled with battery storage. The transfer from the energy carrier at the station to on-board storage in the vehicle accounts for 9% and 12% of the total energy losses of these two modes, respectively. Slow charging modes can achieve a charging infrastructure efficiency of 78% with residential energy storage systems coupled with AC chargers.