Nanoporous framework materials are a promising class of materials for energy-efficient technology of xenon/krypton separation by physisorption. Many studies on Xe/Kr separation by adsorption have focused on the determination of structure/property relationships, the description of theoretical limits of performance, and the identification of top-performing materials. Using high-throughput screening techniques, we evaluated the selectivity of 12,020 Metal-organic Framework (MOF) materials regarding the adsorption of Xe and Kr at different pressure conditions. These selectivities were correlated to key thermodynamic features such as enthalpy and entropy to better understand the thermodynamic origins of the best suited materials for xenon/krypton separation. We observed that the separation process is generally enthalpic in nature and the performance can vary dramatically from low to ambient pressure. Detailed study on a few archetypal structures tried to shed a light on the underlying microscopic mechanisms behind the change of performance between different pressure conditions. Population of different adsorption sites, or repacking of the adsorbed phase at higher loading, can lead to drastic changes in the overall selectivity. The mechanisms behind selectivity at high pressure are complex and unique to each framework, requiring a good understanding of the interactions between guest molecules constrained in the nanopores.