Technology for measuring 3D genome topology is increasingly important for studying gene regulation, for genome assembly and for mapping of genome rearrangements. Hi-C and other ligation-based methods have become routine but have specific biases. Here, we develop multiplex-GAM, a faster and more affordable version of genome architecture mapping (GAM), a ligation-free technique that maps chromatin contacts genome-wide. We perform a detailed comparison of multiplex-GAM and Hi-C using mouse embryonic stem cells. When examining the strongest contacts detected by either method, we find that only one-third of these are shared. The strongest contacts specifically found in GAM often involve 'active' regions, including many transcribed genes and super-enhancers, whereas in Hi-C they more often contain 'inactive' regions. Our work shows that active genomic regions are involved in extensive complex contacts that are currently underestimated in ligation-based approaches, and highlights the need for orthogonal advances in genome-wide contact mapping technologies.