There are many more variables to correct for than just population density but this study does a pretty good job covering that and then some. In short, yes cities have significantly more crime (both violent and property) than rural areas.

https://kb.osu.edu/bitstream/handle/1811/86153/IJRC_Ward-eta...

There are huge numbers of trends in the crime data depending on you want to look at it, so I'm always open to changing my mind on topics like this, if there is good data to support it.

> The average number of residents age 14 - 17 for urban counties was 10,879.74 (SD = 25,923.60), far larger than the mean of 987.32 (SD = 760.86) for rural counties. Likewise, the average number of residents age 18 - 24 for urban counties (18,752.97, SD = 41,994.59) was much greater than rural counties (M = 1,625.68, SD = 1,417.78).

If there are literally 10 times fewer young people, it’s not too surprising that the rural counties had fewer crimes per capita. With that big a disparity it’s kind of shocking that the urban crime rate is only 50% higher.

I hadn’t realized that US rural counties have so few young people. It sounds like the population of those places is on the verge of collapse.

If the median age in rural counties is ~40, there are few small children, but only 2.5% of the people are 14–24, it sounds like there must be a pretty large number of 25–40 year olds though. Has there just been a sharp demographic break within the last generation with all of the young people suddenly moving away, or are large numbers of 30-somethings moving from the city to rural towns?

> the population of those places is on the verge of collapse.

That collapse has been underway for a couple of generations now.

>Has there just been a sharp demographic break within the last generation with all of the young people suddenly moving away, or are large numbers of 30-somethings moving from the city to rural towns?

Depending on how you count, young people have been leaving farms for 4 or 5 generations now. Part of this is down to the increased efficiency of agriculture, which means fewer people are needed to produce food, which means fewer agricultural jobs. Most job creation happens in cities now, so young people who are not inheriting a family business tend to move toward cities. Richard Florida and others have written extensively about this demographic shift.