There has been widespread adoption of downscaled products amongst practitioners and stakeholders to ascertain risk from climate hazards at the local scale. Such products must nevertheless be consistent with physical laws to be credible and of value to users. Here we evaluate statistically and dynamically downscaled products by examining locally relevant covariances between downscaled temperature and precipitation during convective and frontal precipitation events. We find that two widely-used statistical downscaling techniques (LOCalized Analogs version 2 (LOCA2) and Seasonal Trends and Analysis of Residuals Empirical-Statistical Downscaling Model (STAR-ESDM)) generally preserve expected covariances during convective precipitation events over the historical and future projected intervals. However, both techniques dampen future intensification of frontal precipitation that is otherwise robustly captured in global climate models (i.e., prior to downscaling) and with dynamical downscaling. In the case of LOCA2, this leads to appreciable underestimation of future frontal precipitation events. More broadly, our results suggest that statistical downscaling techniques may be limited in their ability to resolve non-stationary hydrologic processes as compared to dynamical downscaling. Finally, our work proposes expected covariances during convective and frontal precipitation as useful evaluation diagnoses that can be applied universally to a wide range of statistically downscaled products. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. LLNL-ABS-866383