LiTaO3 and LiNbO3 crystals are investigated here in a combined experimental and theoretical study that uses Raman spectroscopy in a complete set of scattering geometries and corresponding density-functional theory calculations to provide microscopic information on their vibrational properties. The Raman scattering efficiency is computed from first principles in order to univocally assign the measured Raman peaks to the calculated eigenvectors. Measured and calculated Raman spectra are shown to be in qualitative agreement and confirm the mode assignment by Margueron et al. [J. Appl. Phys. 111, 104105 (2012)], thus finally settling a long debate. While the two crystals show rather similar vibrational properties overall, the E-TO9 mode is markedly different in the two oxides. The deviations are explained by a different anion-cation bond type in LiTaO3 and LiNbO3 crystals.