The paper examines and compares the potential of storage in batteries versus demand response strategies for electricity bill reduction in the residential sector, in the context of the new trend of installing PV systems for self-consumption. The performances of the two methodologies are investigated by applying them to the data of a real household which owns a small solar photovoltaic installation. The benefits of storage and demand response are evaluated through an optimization analysis with a linear programming algorithm. The simulations are carried out both for real market prices of the equipment and for reduced ones, to simulate the case of strong technological development and the corresponding price decrease in the coming years. The electricity pricing scheme is a dual tariff regime modeled according to the Portuguese current rules. The results suggest that at the moment, demand response should be preferred with the current market prices of the hardware. However, a significant decrease in the batteries price can make storage an interesting alternative, especially for the cases in which demand response is not easily applicable.