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Comparing binding sites as geometric solids can reveal conserved features of protein structure that bind similar molecular fragments and varying features that select different partners. Due to the subtlety of these features, algorithmic efficiency and geometric precision are essential for comparison accuracy. For these reasons, this paper presents pClay, the first structure comparison algorithm to employ fine-grained parallelism to enhance both throughput and efficiency. We evaluated the parallel performance of pClay on both multicore workstation CPUs and a 61-core Xeon Phi, observing scaleable speedup in many thread configurations. Parallelism unlocked levels of precision that were not practical with existing methods. This precision has important applications, which we demonstrate: A statistical model of steric variations in binding cavities, trained with data at the level of precision typical of existing work, can overlook 46% of authentic steric influences on specificity (p <= .02). The same model, trained with more precise data from pClay, overlooked 0% using the same standard of statistical significance. These results demonstrate how enhanced efficiency and precision can advance the detection of binding mechanisms that influence specificity.