We use molecular dynamics simulation to investigate polarizability anistropy relaxation in two polar liquids, methanol and acetonitrile, which have similar dielectric constants at room temperature, but are very different at the molecular level. Interaction-induced contribution to the polarizability is included using first-order perturbation theory and separated into a component which projects along the sum of molecular polarizability anistropies and relaxes through collective reorientation and a "collision induced" component which relaxes through other mechanisms involving mainly translational motion. We find that interaction-induced effects on the polarizability anisotropy time correlation are important on all relevant time scales, especially for the more polarizable acetonitrile. In methanol, even though most of the molecular polarizability is along the CO bond, we find that the OH bond dynamics make a substantial direct contribution to polarizability anisotropy relaxation. We compare our results to the experimentally determined nuclear portion of the optical Kerr effect response and discuss their implications for the use of this response in solvation dynamics theories. We find that the short-time optical Kerr response of acetonitrile is dominated by collision-induced polarizability dynamics, while librational orientational dynamics is the main contributor for methanol.