Selective sorption of volatile aromatic compounds is a challenging issue for their total abatement. Despite the well-known affinity of palladium toward rich π systems, studies dedicated to volatile organic compound (VOC) capture with Pd(II)-based metal–organic frameworks (MOFs) are still very scarce. Intending to shed more light on this complex topic, this work compares the adsorption properties of two isostructural MOFs [Cu(2-pymo)2]n and [Pd(2-pymo)2]n and their selectivity for the sorption of linear, cyclic, or aromatic VOCs. The combination of both experimental and computational investigations highlights an increasing aromatic affinity over saturated hydrocarbons when palladium is chosen as a metal center (nBenzene/nn-hexane = 1.8 at 0.5 p/p0) in the MOF instead of copper (nBenzene/nn-hexane = 0.7 at 0.5 p/p0). Furthermore, [Pd(2-pymo)2]n clearly exhibits preferential adsorption of benzene over toluene (nBenzene/nToluene = 1.7 at 0.5 p/p0), due to the steric hindrance effects of the latter. The present results clearly underline the attractiveness of Pd-based MOFs for the design of selective aromatic adsorbents. Moreover, they also highlight the [Pd(2-pymo)2]n MOF as a relevant candidate for the selective capture of benzene, by a synergistic combination of both charge interactions and steric hindrance effects.