The Leica 180mm f/2.8 APO-Elmarit-R has a cult following among Nikon and Canon users (converted for Nikon or with an adapter for Canon). I bought mine some years ago brand-new (latest variant), back when it was still in production.
Previously presented were the doll's comparison and the rulers comparison, but these were at close range and could be expected to favor the Sigma, which is presumably optimized as a macro lens, while the Leica 180/2.8 APO-Elmarit-R is presumably optimized for medium and long distance.
This demanding planar comparison was shot meticulously, with seven focusing series for the Leica and three for the Sigma with cross checks to be sure of the results. I consider the results definitive for anyone looking to choose between these two lenses. But with both lenses, there is a fly in the ointment.