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Solders for the most part get much more time and training using firearms than police who tend to have a much wider range of duties to perform.

Most NATO militaries have increased the amount of training in urban environments. I'm pretty sure(or overly optimistic) they have decent training/drilling experience as the political backlash from having soldiers get way to aggressive in terms of resorting to military tactics vs police tactics.

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They are much better marksmen, it's true. But police have waaaaaay more experience dealing with drunk idiots, mentally ill people, people doped up to their eyeballs on speed and so on. Deciding whether someone is one of these or a serious security threat is not as easy as it might sound, hence my curiousity vis-a-vis the rules of engagement...

The Australian military is generally lauded as being excellent at peace-keeping operations, yet during officer training, it was hammered into us that policing was a much harder operation, and that our hierarchy would never accept policing missions.