A book chapter by Alan Krueger in an NBER volume from 1988 discusses trends in earnings. A big part of his analysis concerns the federal worker bonus. The last paragraph summarizes his findings on state and local government workers' earnings:
At the state and local government level, both the longitudinal and cross-sectional analyses suggest that the differential in earnings between public and private sector workers was small and positive in the 1970s, but became negative by the mid-1980s. Furthermore, the empirical analysis finds no evidence of a difference in pay between union and nonunion members in the public sector.
One of the big changes since the 1980s has been the movement away from defined-benefit pensions in the private sector and toward defined-contribution plans. I think the primary difference between them is the amount of risk, and not the average level, but a larger issue today may be differences in post-retirement compensation for public versus private workers. Health insurance copays may be a big part, but pensions might be as well.