We present a molecular dynamics study of the solvation properties of the tetrahedral AsPh4+ and BPh4- ions in water and chloroform solutions. According to the "extrathermodynamic" TATE (telraphenylarsonium tetraphenylborate) hypothesis, these nearly isosterical ions have identical free energies of solvation in any solvent, as the latter are generally assumed to display little dependence on the details of the charge repartition, provided that the total +/- charge is delocalized and that the ion's periphery is relatively inert. We compare eight different sets of charges obtained consistently for both ions and find that the anion is always better hydrated than the cation, as evidenced by ion-solvent interaction energies and changes in free energies of ion charging. This is explained by specific OH-Jr bridging interactions in the anion and the positive electrostatic potential at the center of the fictitious AsPh40 and BPh40 all-neutral species. With all models, the cation is also predicted to be more easily transferred from water to dry chloroform. The conclusions obtained with standard solvent models (TIP3P water and OPLS chloroform) are validated by tests with the polarizable Wallqvist and Berne water model and the Chang et al. chloroform model, and with computer simulations on a "wet chloroform" solution. The recently developed TIP5P water model yields, however, much closer hydration energies of AsPh4+ and BPh4-. The importance of "long-rangre" electrostatic interactions on the charge discrimination by solvent is demonstrated by the comparison of standard vs corrected methods to calculate the Coulombic interactions. These results are important in the context of the "TATB hypothesis" and for our understanding of solvation of large hydrophobic ions in pure liquids or in heterogeneous liquid environments.