Microscopic diffusion processes (such as radiative levitation, gravitational settling, and thermal diffusion) in the outer layers of stars are important because they may give rise to surface abundance anomalies. Here we compare radiative accelerations (g_rad) derived from the new Opacity Project (OP) data with those computed from OPAL and some previous data from OP. For the case in which we have full data from OPAL (carbon, five points in the rho-T plane), the differences in the Rosseland mean opacities between OPAL and the new OP data are within 12% and are less than 30% between new OP and previous OP data (OP1). The radiative accelerations g_rad differ at up to the 17% level when compared to OPAL and up to the 38% level when compared to OP1. The comparison with OP1 on a larger rho-T space gives a difference of up to 40% for g_rad(C) and increases for heavier elements, reaching 60% for Si and 65% for S and Fe. We also constructed four representative stellar models in order to compare the new OP accelerations with prior published results that used OPAL data. The Rosseland means overall agree better than 10% for all our cases. For the accelerations, the comparisons with published values yield larger differences in general. The published OPAL accelerations for carbon are even larger relative to OP compared to those that our direct comparisons indicate. Potential reasons for this puzzling behavior are discussed. In light of the significant differences in the inferred acceleration rates, theoretical errors should be taken into account when comparing models with observations. The implications for stellar evolution are briefly discussed. The sensitivity of g_rad to the atomic physics may provide a useful test of different opacity sources.