We describe the construction and performance of dye-sensitized solar cells (DSCs) based on arrays of ZnO nanowires coated with thin shells of amorphous Al2O3 or anatase TiO2 by atomic layer deposition. We find that alumina shells of all thicknesses act as insulating barriers that improve cell open-circuit voltage (VOC) only at the expense of a larger decrease in short-circuit current density (JSC). However, titania shells 10-25 nm in thickness cause a dramatic increase in VOC and fill factor with little current falloff, resulting in a substantial improvement in overall conversion efficiency, up to 2.25% under 100 mW cm(-2) AM 1.5 simulated sunlight. The superior performance of the ZnO-TiO2 core-shell nanowire cells is a result of a radial surface field within each nanowire that decreases the rate of recombination in these devices. In a related set of experiments, we have found that TiO2 blocking layers deposited underneath the nanowire films yield cells with reduced efficiency, in contrast to the beneficial use of blocking layers in some TiO2 nanoparticle cells. Raising the efficiency of our nanowire DSCs above 2.5% depends on achieving higher dye loadings through an increase in nanowire array surface area.