With correct statistics (comparing equal education and experience levels), it turns out that the private sector pays more.
You forgot the bribes. BTW, having conducted numerous salary surveys entry level jobs and up about two levels the government jobs pay about 40% more(total comp). It evens out at manager level, and declines at the top levels(bribes start coming in). Which is why government is incompetent, inefficient, and corrupt. Happens in the private sector too, but then those companies die.
Your comment is at odds with a number of recent studies. Do you have any numbers to back up your comment? I have 2 sources. Go to Heritage Foundation or BUreau of Economic Analysis.
According to BEA: Federal civil servants earned average pay and benefits of $123,049 in 2009 while private workers made $61,051 in total compensation, according to the Bureau of Economic Analysis. The data are the latest available.
There are few guaranteed pensions in private sector not to mention guaranteed jobs or bonuses. When times are good, the private sector may adjust up to compete for top workers, but they also hire those over qualified in tough times. The government does not lay off, does not cut pensions, could care less about profit/loss/revenue—all laws of the economic cycle under which businesses must live.
With the proper selection of the statistics used, I'm quite certain that you could conclusively "prove" either to be the case.