Abstract The concept of surface-flux transport (SFT) is commonly used in evolving models of the large-scale solar surface magnetic field. These photospheric models are used to determine the large-scale structure of the overlying coronal magnetic field, as well as to make predictions about the fields and flows that structure the solar wind. We compare predictions from two SFT models for the solar wind, open magnetic field footpoints, and the presence of coronal magnetic null points throughout various phases of a solar activity cycle, focusing on the months of April in even-numbered years between 2012 and 2020, inclusively. We find that there is a solar-cycle dependence to each of the metrics considered, but there is not a single phase of the cycle in which all the metrics indicate good agreement between the models. The metrics also reveal large, transient differences between the models when a new active region is rotating into the assimilation window. The evolution of the surface flux is governed by a combination of large-scale flows and comparatively small-scale motions associated with convection. Because the latter flows evolve rapidly, there are intervals during which their impact on the surface flux can only be characterized in a statistical sense, thus their impact is modeled by introducing a random evolution that reproduces the typical surface flux evolution. We find that the differences between the predicted properties are dominated by differences in the model assumptions and implementation, rather than the selection of a particular realization of the random evolution.