Hydrostatic pressure is a common perturbation to probe the conformations of proteins. There are two common forms of pressure-dependent potentials of mean force (PMFs) derived from hydrophobic molecules available for coarse-grained molecular simulations of protein folding and unfolding under hydrostatic pressure. Although both PMFs include a desolvation barrier separating the direct contact well and the solvent-mediated contact well, how these features vary with hydrostatic pressure is still debated. There is a need for a systematic comparison of these two PMFs on a protein. We investigated the two different pressure-dependencies on the desolvation potential in a structure-based protein model using coarse-grained molecular simulations. We compared the simulation results to the known behavior of proteins based on experimental evidence. We showed that the protein's folding transition curve on the pressure-temperature phase diagram depends on the relationship between the potential well minima and pressure. For a protein that reduces its total volume under pressure, the PMF needs to carry the feature that the direct contact well is less stable than the water-mediated contact well at high pressure. We also comment on the practicality and importance of structure-based minimalist models for understanding the phenomenological behavior of proteins under a wide range of phase space.