I can't speak to the American federal context, but in the Canadian context (visible from the Canuck equivalent of the FEVS: http://www.tbs-sct.gc.ca/pses-saff/index-eng.asp ), women are more numerous in the PS than men. They also tend to enjoy slightly higher promotion rates. One of the principal reasons for that is simply the type of work that men and women tend to cleave to. For example, blue collar work is primarily sought by men, and has the misfortune to be largely situated in regional/district oiffices, rather than the capital, such that promotional opportunities are limited. In contrast, a great deal of what transpires in the national capital is the sort of office admin work that women preferentially seek. HR, for example, is something like 3/4 female, and is mostly found in the capital. Given that the national capital region has the largest single concentration of job opportunities, and that there is a great deal of agency-to-agency mobility, women tend to find themselves in the enviable position of being in the place where you can move around and there are lots of places and levels to move to. As a result, they tend to have a slightly higher promotion rate than men, as you can see from Q78 here: http://www.tbs-sct.gc.ca/pses-saff/2011/results-resultats/bq-pq/00/... That gap is starting to decrease in recent years with various hiring freezes imposed (also visible from the same table).
Naturally, not all promotions are alike, and I would not dream of equating a move from the lowest to second lowest admin-support pay grade with movement from one of the policy-stream feeder groups to the executive group. The survey info I've linked you to is only at the aggregate level, and doesn't permit drilling down to examine upward mobility, by sex, from level to level.
RE: gender differences in thinking. Having followed all that Carol Gilligan "In a different voice" stuff since the early 80's, my sense is that it tends to get overblown the way that all the right-brain/left-brain stuff does; i.e., it's much less pronounced than popular writers would have us believe. Certainly people tend to specialize as they get older, and we should not be surprised that individual differences in reasoning can become starker, but a great many researchers will tell you that, despite the two sexes not being identical, differences within each sex are generally much wider than differences between the sexes.
Aging theorist David Gutman has also proposed that men and women become more similar to each other as what he terms "the parental emergency" ends in mid-life ( http://books.google.ca/books/about/Reclaimed_Powers.html?id=kNpI9ah... ). Gutman takes the rather interesting view that gender roles are a culturally evolved adaptation to the need for division of the household labour related to child-rearing. We get socialized/prepared for that role division during our formative years, and once the kids are grown up, we essentially take those cloaks off, and return back to who we are.
I introduce this digression because when we begin any discussion of male-female differences in the workplace, there is an underlying assumption that men are men and women are women, in exactly the same form, across their entire working lives. It may well be the case that whatever "gender intelligence" exists in the workplace is a transient expression that the overall culture moves us into and out of. So we may be well within our rights to talk about gender differences when talking about those under 40, but are wasting our breath when discussing those employees who are 45 and older.
There is also something to be said for the personality types that desire to be management. Personally, I think that is a "type" that trumps a lot of any reliably observed differences between men and women. I.E., somebody who really wants to be management is neither representative of all men or all women. Having spent my entire life - but for two summers as a student - in the public sector, I can't speak with authority to public-private differences, but I suspect that while the expectations of upward mobility may be different between the sexes, and maybe the sectors, once seized, the urge towards upward mobility blurs most divisions between the sexes.