We present an experimental investigation of methylammonium lead tribromide single crystals in the orthorhombic, tetragonal, and cubic phases based on inelastic and deep inelastic neutron scattering experiments. We show how the average hydrogen nuclear kinetic energy, mainly affected by zero-point vibrational energies, shows differences larger compared to the changes simply related to temperature effects when moving from one phase to another. In particular, the Gaussian contribution to the average nuclear kinetic energy is larger in the tetragonal phase compared to the cubic and orthorhombic ones. Moreover, we find that the vibrational densities of states of MAPbBr3 single crystals in the orthorhombic phase are compatible with previously reported results on powder samples, and that the only vibrational modes that show slightly different frequencies compared to MAPbI3 are those in the energy range between 100 and 300 cm-1, related to librational/rotational modes. As these shifts are of about 10 cm-1 and do not affect any higher-energy vibrational mode, we conclude that the zero-point energies and average nuclear kinetic energies in the two-hybrid organic/inorganic perovskites are expected to be approximately the same within a harmonic framework.