As someone who has straddled the worlds of law enforcement and an Army at war, let me be the first to say that the two animals are very different. You would get a different idea from talking to the number of combat veterans who have returned from Iraq and Afghanistan. To many of them, the two worlds are inseperable, and that's problematic.
After the wars are over and veterans return from their tours, the first question asked is 'what am I going to do with my life?' more often than not. Leaving the military of your own free will is difficult choice that isn't taken lightly. If you're a 22 year old who joined the military right out of high school, for four years your housing, your food, your medical care was always taken care of. You always had a pay check coming in, you always had someone there when you needed to drink, and if you got in trouble you would be taken care of. Your bad habits are often excused, and the Army will always be there to love you, no matter what. It is a seductive world. When you leave that behind and face the world on your own two feet, it can be frightening.
It does not surprise me that many veterans find respite in law enforcement. There are similarities there culturally and otherwise, and a sense of discipline that the usual nine to five doesn't have. However, in taking in these veterans, many law enforcement departments let the military culture override the policing culture. This is problematic in a variety of ways.
First, the rules of engagement in a war zone compared to the United States are entirely different monsters once you get past the superficial similarities. When veterans bring their ROE mentalities to the Use of Force template, they're more often than not going to get hammed up. A lot of the basic policing skills, such as interpersonal conversation and observation skills seem to get replaced with 'do what I tell you to because I said so' and judging everything through the context of searching for an IED.
Not that there isn't a time to go all Boss Hoss, but there's something to be said for not turning every vehicle stop into Ruby Ridge. However, the biggest positive I've seen from us veterans coming in is that training has evolved massively from the old days of 'square up with target, shoot' as many of us have seen the elephant and are unwilling to put our lives in the hands of shit that does not work. However, I think we can do with less of the digicam uniform bullshit, the trying to be 'operators' with cool guy shades and patches on everything. The biggest threat to law enforcement is complacency, not lacking mirror shades. If law enforcement officers could remember that instead of worrying about looking like the Special Response Team we'd all be a lot safer.