Ionic surfactants are known to build up higher interfacial pressures at oil/water interfaces than at air/water interfaces for the same surfactant bulk concentration. Here, we systematically investigate this effect through atomistic molecular dynamics (MD) simulations of surfactant-loaded air/water and oil/water interfaces. Two prototypical ionic surfactants, C12TAB and sodium dodecyl sulfate (SDS), are studied and found to give consistent results, which are also robust with respect to variations in the simulation force field. The simulations reproduce the experimental interfacial pressure data on a semiquantitative level and reveal that the influence of oil on the surfactants' in-plane distribution is a major contribution to the observed effect, albeit insufficient to be the sole reason. The simulations are further analyzed with regard to surfactant/oil cooperative/competitive effects that have been invoked recently as an explanation. However, the interfacial orientation of oil molecules, a presumable indicator for such behavior, is found to display changes only for high levels of surfactant coverage.