I'd have thought physical size is less important than population, but I dunno how that'd work in practice. Although the major European countries are physically smaller than most US states, each has a bigger population than almost all of them. But the EU and US are not the same as much as some people are seemingly calling for a "United States of Europe": there'll be more *exits before that comes to pass.
Here in the UK there are a number of police forces which are geographic but don't necessarily follow any county lines: here in Oxford we have Thames Valley Police which is pretty much what it sounds like, except for the bit of the Thames Valley where London is which has the Metropolitan Police. In other places I've lived there's the likes of Northumbria Police (Northumbria hasn't existed as a specific place for most of the past 1,000 years, but it covers some of the region in question) and Essex Police which is a county force. They have some differences when it comes to stuff like traffic policing policy and so on but they're all much of a muchness in terms of how the law is applied. And that's pretty much it.
There are some specific non-geographical policing organisations like British Transport Police and the Military Police who have specific duties: they usually work within that remit so the military police will police the military (rather than the military doing the policing which is a temporary arrangement in emergency situations such as now) but have the same powers as the regular constabularies wherever they happen to be involved.
And that's it, pretty much. The US system is something that looks absolutely confusing to me, with local sheriffs, state police, the FBI and others who often seem to disagree not over points of law but rather territory, and it seems to an outsider that the disagreements tend to become quite entrenched even when one technically has authority over the other. And then there're the ones who don't seem to fit into that system at all: an acquaintance was nicked for speeding when we were over there and got pulled by a "state trooper". We'd already been warned about them as they have a habit of shooting people, apparently. And also not to get out of the car if we're pulled over because that turns out to be a guaranteed way of being shot. eek.
