A lot of the standard stuff always factors in: they wake up early, they work hard, they can perform under stress, they can lead, they're aggressive, they work in teams, etc. All that is generally true, I would say, but I would emphasize generally. The military is comprised of all types. The closer people are to the military, the more they tend to understand that -- it's noble to raise your right hand, but it doesn't, and shouldn't, mean the world owes you a red carpet rollout from there afterwards. If you're upset about the demand fee on your excise tax, I feel your pain, but the minute you tell me that your four-year enlistment in the late 1980s means you "deserve better," you've lost points in my book!
But anyway, back to my point. Here's one benefit of military experience that doesn't make its way into a lot of the boilerplate 'let's hire vets' material -- it gives you a valuable understanding of organizational structure.
Maybe that could come from other places, too -- at a big corporation like GE or IBM, you'd probably get a similar foundation in how the various roles and responsibilities, i.e. the 'lanes in the road' come together to make the whole thing work. But you're guaranteed to get that in the military. From an E-1 boot Private to an O-10 General, you learn your sense of role and place, which means not just what you do, but also what you don't do, because it's handled by someone else. Put the whole thing together, and it all works (on paper, at least).
You also get a sense of frustration with bureaucracy. That's important, because if you're a highly-motivated individual, you learn what NOT to do (mindlessly pawn people off to 'someone else') and learn the real value in closing the loop and checking back up. In customer service, there's nothing someone would rather hear than "I got it" or at least "I'll tell you who 'got it' and make sure they get in touch with you." People know when they're just being transferred into a black hole, and they rightfully resent it.
I *shipped off* in 2004, and the job I have now is the first I've had since then that doesn't require a particular uniform, haircut, and shave. A substantial chunk of what I do (say, 25 percent) is traffic control. People have issues, concerns, problems, questions, etc. and they wind up on the other end of the phone, or in the inbox -- either because they went straight to what seemed like a logical choice, or because another department shunted them off to the second floor. In most cases, I don't have the power to solve their issue, but I can get their info, put it in our spreadsheet, figure out where to go with it, and then follow-up, either with the person or with the department that took it.
The follow-up is key. Last week, a guy really let me have it (subject: bleachers at Alumni Field) for what seemed like ten straight minutes on the phone. I didn't create the problem, and didn't have the power to solve it, but the guy didn't care. The amazing thing, though, was that after the guy had let off a lot of steam, he took and breath, completely changed his tone and said [in a much calmer, more rational sort of way], "You know what? I think this whole situation sucks, but I'm really glad you got back to me to let me know about the city's decision. I really appreciate that."
I could totally relate to the guy. I've fought so many bureaucratic mini-struggles over the past 7+ years (and I'm fighting one now about the Reading-to-Devens unit transfer that I'm trying to push through) that I know how much it sucks to be ignored by the person who should be helping you through. Everyone with even a modicum of maturity knows the world isn't perfect. Sometimes things take time, sometimes bleachers need to be removed on safety grounds, and yes, sometimes the graffiti doesn't get removed from the side wall of the Superior Court.
Everybody *gets* that. They get the system, and they get the process, but they just want the basic respect that comes from someone saying, "I've got it. You matter, and you're not being blown off."
And back to the 'lanes in the road' issue -- that understanding is what keeps any earnest person in the system from really screwing things up by trying to be a hero and do things that should be done by someone else.
No CEO or ex-General or President is ever going to get up and say, "Dammit! I want to see more veterans get hired because they understand organizational structure and can distinguish good bureaucrats from bad ones!"
But if someone ever does, I'll be the guy hitting the 'Like' button.