I agree that in a not so distant past, the mil guys did a better job of networking and passing on the intel. The nature of the flying squadrons (my own background) is that you are likely to know far more about even the clowns you don't like than what you are likely to know about just about anyone if you matriculate via the civilian route. I still think that there are two big discriminators in application and interview success: 1) Mil guys tend to look at the new world of civilian flying as unknown enemy territory, and they invest far more in the research, practice, and paid outside help to navigate the application and interview process. There is a lot to be said for the variety of commercial application and interview prep services, and my (limited) experience is that civilian only pilots tend to discount the value of these companies more frequently, often because they're "already doing the same job." 2) To the degree that it matters, companies value the military trained pilots because of its history as a sink or swim proposition (not to say that hasn't changed or some clowns have gotten through). Contrast that with the wickets of getting your ticket as a civilian only ($$$ and time), and they feel an assurance (I'm open to the argument that it's misplaced) that surviving military pilot training and military flying is a good discriminator to rely upon.

I would say that civilians have one advantage that military pilots do not: time flexibility. The commitment to active duty after pilot training and the service commitments after moves, or the need to be current in the cockpit, create a strong element of lucky timing for many military guys that a pilot at a regional, 135, etc. doesn't need to worry about in the same way (2 weeks notice). Certainly not a perfect system, but not really stacked with a decisive advantage one way or another.