I have found that the difference between the two to be down to the more aggressive role of the military guys. Looking after a Brigadier in places like Helmund is always going to be a lot more dangerous than a high ranking politician in London. The police have to justify every single round fired, whereas guys in the Mil may not have to (hence the use of belt fed weapons, 40mm HE etc), despite what the ROE may state, obviously common sense and moral standing will always dictate your actions. I worked with a couple of tone's guys in kabul, a few years ago and they were good guys. One was frustrated at their units reluctance to get some serious weapons (5.56mm +) for them despite some of the locations they were now required to operate in since 9/11. They told me that assault rifles were seen as too aggressive for their role. I can understand that in the UK, but when you are in Iraq/A'Stan, then a semi auto only MP5 is about as much use as a chocolate fireguard.
I'm sure there will be more opinions on this subject from both camps, but the military have it in my book as it is easier to tone things down, but hard to turn it up if you haven't had that training in the first place.