Transition metal phosphorous trichalcogenides, MPX_{3} (M and X being transition metal and chalcogen elements, respectively), have been the focus of substantial interest recently because they are unusual candidates undergoing Mott transition in the two-dimensional limit. Here we investigate material properties of the compounds with M=Mn and Ni employing ab initio density functional and dynamical mean-field calculations, especially their electronic behavior under external pressure in the paramagnetic phase. Mott metal-insulator transitions (MIT) are found to be a common feature for both compounds, but their lattice structures show drastically different behaviors depending on the relevant orbital degrees of freedom, i.e., t_{2g} or e_{g}. Under pressure, MnPS_{3} can undergo an isosymmetric structural transition within monoclinic space group by forming Mn-Mn dimers due to the strong direct overlap between the neighboring t_{2g} orbitals, accompanied by a significant volume collapse and a spin-state transition. In contrast, NiPS_{3} and NiPSe_{3}, with their active e_{g} orbital degrees of freedom, do not show a structural change at the MIT pressure or deep in the metallic phase within the monoclinic symmetry. Hence NiPS_{3} and NiPSe_{3} become rare examples of materials hosting electronic bandwidth-controlled Mott MITs, thus showing promise for ultrafast resistivity switching behavior.