An interesting topic that I had not seen in The Hive before but popped up on the list today because someone deleted something. Not sure if you are still interested in your question above but if you are look at the link below.
I will declare first that I was a Federal employee only once, that during a stint in the Peace Corps in the 1970's. I will put a link to a CBO report from 2012 comparing compensation levels between the private sector and Federal employees. The cover page shows the differences for the five educational levels going from HS or less, some college, bachelor's, masters, and professional or doctoral degree. There is a stacked bar graph that shows both direct salary and benefits packages. The summary is that Federal employees do better than their private counterparts financially except for those at the highest educational rung who do worse than the private sector. The advantages of the Feds over the private sector are greatest for the two lower educated groups and for those with bachelor's or master's degrees their salary advantage is negligible and the advantage is only in benefits. I would interpret this as showing that for blue collar type work the Federal empoyees have avoided much of the downward pressure on compensation that has come with deunionization and deindustrialization. However, I also suspect that many of the lower paying Federal jobs such as cleaners, cafeteria workers, etc. may have been contracted out and taken out of the Federal mix. Those last two sentences are speculation and not based on hard fact so I am more than willing to be corrected on that.
As far as the decline of labor and the increase in inequality, they certainly have happened at the same time and I suspect they are related. There is a lot of talk about high paying industrial jobs. There is nothing written that industrial jobs are high paying - just look at the history of labor in the early 20th century and the violent efforts to put down the labor movement or look at the salary of people sewing clothes in Bangladesh. Unionized jobs are potentially high paying. The problem to me seems to be not the service economy, but the fact that the service economy is much more difficult to organize. My solution would be since it is harder to organize a union, then Big Brother government sets the baseline. But that is a bit of a different topic.