Battery energy storage systems (BESSs) for residential photovoltaic (PV) prosumers are becoming more popular with the reduction of battery prices, as a means of increasing self-consumption. When considering prosumers that also own an electric vehicle (EV), smart charging can also fulfill the same objective. This paper assesses the benefits of a PV prosumer with an EV under two options: installing a BESS or applying smart charging. Smart charging is applied with the goal of reducing energy imports by charging the EV when there is excess of production. The effect of using a BESS of varying inverter and storage size is also investigated, when operated under a simple energy import minimization logic. We use a yearly dataset of real 5-min measurements collected from a Danish household with a 6 kWp PV plant. The prosumer also owns a 62 kWh Nissan LEAF. We find that smart charging increases self-consumption from 29% to 54%, leading to yearly savings of 220 e . Through a sensitivity analysis we find that a BESS of 8 kWh / 2 kW yields similar yearly results. Given the approximately 20 times higher payback period of the BESS, we conclude that smart charging is economically much more attractive.