A lot of the "who's up? who's down?" reporting on administration officials is just gossip. It's fun for us outsiders to read, but not necessarily reliable. Nevertheless, sometimes these stories have nuggets of fact that help to confirm their theses.
Last March the Financial Times ran an excellent piece describing the Obama National Security Council and revealed that the Deputies Committee, the #2's in each department, met 270 times in the first year, which would work out to once almost every single weekday. I still believe the number, and conclude that the NSC process was very active under Obama and General Jones.
That same article made the point that Secretary Gates and Secretary Clinton had developed a "strong working relationship" that helped them in dealing with their colleagues. A new article in Politico makes the same point, and cites a congressman as saying that they present a united front and speak "seamlessly and ... on the same page" in joint closed door briefings on the Hill. This, of course, is a sharp and welcome contrast with several previous administrations.
Instead of psychological explanations for why the two cabinet officers work together so well, just remember that it is in each one's interest to do so. Their alliance and cooperation enables each to accomplish more of what they want to achieve.