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To study the global hydrological cycle and its response to a changing climate, we rely on global climate models (GCMs) and global hydrological models (GHMs). The spatial resolution of these models is restricted by computational resources and therefore limits the processes and level of detail that can be resolved. Increase in computer power therefore permits increase in resolution, but it is an open question where this resolution is invested best: in the GCM or GHM. In this study, we evaluated the benefits of increased resolution, without modifying the representation of physical processes in the models. By doing so, we can evaluate the benefits of resolution alone. We assess and compare the benefits of an increased resolution for a GCM and a GHM for two basins with long observational records: the Rhine and Mississippi basins. Increasing the resolution of a GCM (1.125 to 0.25 degrees) results in an improved precipitation budget over the Rhine basin, attributed to a more realistic large-scale circulation. These improvements with increased resolution are not found for the Mississippi basin, possibly because precipitation is strongly dependent on the representation of still unresolved convective processes. Increasing the resolution of the GCM improved the simulations of the monthly-averaged discharge for the Rhine, but did not improve the representation of extreme streamflow events. For the Mississippi basin, no substantial differences in precipitation and discharge were found with the higher-resolution GCM and GHM. Increasing the resolution of parameters describing vegetation and orography in the high-resolution GHM (from 0.5 to 0.05 degrees) shows no significant differences in discharge for both basins. A straightforward resolution increase in the GHM is thus most likely not the best method to improve discharge predictions, which emphasizes the need for better representation of processes and improved parameterizations that go hand in hand with resolution increase in a GHM.