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Molybdenum ditelluride (MoTe₂) has attracted significant research interest due to the discovery of exotic topological states and pressure-driven superconductivity. First-principles calculations combined with the anisotropic Migdal-Eliashberg formalism have been carried out to investigate the role of electron-phonon interaction and the superconducting pairing mechanism in the two structurally similar phases, T_d and 1T’, under pressure. We find that both phases are superconducting, with the centrosymmetric 1T’ phase displaying a slightly larger electron-phonon coupling strength compared to the non-centrosymmetric T_d phase due to the softening of the low-energy phonon modes and a small increase in the density of states at the Fermi level.