The effect of domain structure on the photovoltaic response of BiFeO3 vertical capacitors is investigated, by domain engineering using vicinal SrTiO3 substrates. It is observed that the open-circuit photovoltage remains unaffected by the domain structure, consistent with the photovoltaic effect being driven by the polarization modulated band bending at the metal/BiFeO3 interface. Nevertheless, the enhancement of short-circuit photocurrent is achieved and attributed to the conducting domain walls. Furthermore, we have estimated and compared the magnitudes of photoconductivity of domains and domain walls in BiFeO3 thin films, which can be used to explain the photocurrent improvements. These findings cast some light on the role of domain walls in ferroelectric photovoltaic effects and provide a simple route towards enhanced efficiency.