Murder rate is a compound of many factors of course. I'd see the ban on firearms and control at the frontiers as the #1 reason there's so few violent crimes. The worse incidents outside of organized crime ducking it out have been people running around with knives, and it that limits a lot the extent of crimes.

In comparison, european countries are more connected and the networks will be a lot more international. For instance Marseille has a kind of violent crime that comes from guns and drugs smuggled at the port that won't happen as much in Japan (Fukuoka is a city of its kind in that regard...)

On police presence, you'll see crime rate similar to Japan in well funded districts that have a very local and always present police. That makes them part or the everyday life, they will be more relaxed, more aware of the oddities and weird behaviors, and residents will also rely on them more as they are familiar instead of being some kind of alien presence.

Of course these cities will also probably spend more on school equipment, libraries, public infra etc. This costs money/taxes that not every city has or is willing to spend.