Electrodeposited Cu2O-ZnO heterojunctions are promising low-cost solar cells. While nanostructured architectures improve charge collection in these devices, low open-circuit voltages result. Bilayer and nanowire Cu2O-ZnO heterojunction architectures are systematically studied as a function of the Cu2O layer thickness, ZnO nanowire length, and nanowire seed layer. It is shown that a thick depletion layer exists in the Cu2O layer of bilayer devices, owing to the low carrier density of electrodeposited Cu2O, such that the predominant charge transport mechanisms in the Cu2O and ZnO are drift and diffusion, respectively. This suggests that the low open-circuit voltage of the nanowire cells is due to an incompatibility between the nanostructure spacing required for good charge collection (<1 mu m) and the heterojunction thickness necessary to form the full built-in potential that inhibits recombination (>2 mu m). The work shows the way to improve low-cost Cu2O cells: increasing the carrier concentration or mobility in Cu2O synthesized at low temperatures.