Rare-earth orthoferrites and orthomanganites present strong couplings between their structural distortions and physical properties, namely magnetoelectricity, generating interest in predicting and realizing new phases under external parameters, such as hydrostatic pressure. In this regard, we discuss the differences and the similarities of the high-pressure behaviour of the structural distortions arising from anisotropic volume compression. This allows a better understanding of the role played by the octahedra tilt and Jahn-Teller effect as pressure accommodation mechanisms on the stabilization of different crystallographic phases after the insulator to metal structural transition occurring at the critical pressures (Pc) between 35 and 50 GPa.