Comparing chromatin contact maps is an essential step in quantifying how three-dimensional (3D) genome organization shapes development, evolution, and disease. However, no gold standard exists for comparing contact maps, and even simple methods often disagree. In this study, we propose novel comparison methods and evaluate them alongside existing approaches using genome-wide Hi-C data and 22,500 in silico predicted contact maps. We also quantify the robustness of methods to common sources of biological and technical variation, such as boundary size and noise. We find that simple difference-based methods such as mean squared error are suitable for initial screening, but biologically informed methods are necessary to identify why maps diverge and propose specific functional hypotheses. We provide a reference guide, codebase, and benchmark for rapidly comparing chromatin contact maps at scale to enable biological insights into the 3D organization of the genome.