Differential solar heating and wind-driven Ekman flow over the Southern Ocean together tilt up isopycnal surfaces across the Antarctic Circumpolar Current. Tilted isopycnals are susceptible to baroclinic instability, and mesoscale eddies have a tendency to homogenize potential vorticity (PV) along isopycnals. Under inertial, statistical steady-state conditions with strong eddies and an associated down-gradient PV flux, transformed Eulerian mean theory suggests that (i) large-scale isopycnal slope is primarily set by the planetary PV gradient and (ii) horizontal and vertical stratification are strongly coupled. Here we employ a simple homogenization metric to test these results using both observational data and output from an eddy-permitting primitive equation model. We find a high degree of homogenization on sufficiently large scales (>1,000 km) in both models and observations, and we observe significant spatio-temporal variability on smaller scales. In a numerical sensitivity experiment, the degree of PV homogenization is moderately sensitive to the perturbation in the surface westerly wind stress. Our results provide insights into the relationship between the interior PV distribution and eddy-induced transport.