Inelastic x-ray scattering measurements of the phonon density of states (DOS) of PuO2(+2%Ga) were made and compared to recent predictions from the literature made using three leading theoretical approaches; Density Functional Theory (DFT), DFT plus the Hubbard U (DFT+U), and Dynamical Mean-Field Theory (DMFT). The DFT prediction, which does not account for strong electronic correlations, underestimates the measured energies of most features. The DFT+U and DMFT predictions, which include approximations to strong correlation effects, more accurately reflect the low energy features but exaggerate splitting in the highest energy optic oxygen modes. The exaggeration of the splitting is worse for DFT+U than for DMFT. The transverse acoustic mode shows the least sensitivity to calculation type, and is well reproduced by all three theories. The longitudinal acoustic mode, which is thought to control the thermal conductivity, is more sensitive to calculation type, suggesting an important role for electronic correlations in making application-critical predictions.