My brother lives in a small town, and kids in his neighborhood shot their kids with BB guns. They have issues with neighbors leaving their dogs off leash and attacking their dogs. They've had people from the neighborhood try to run them off the road. None of these things get reported to the police, because the police won't do anything, and you'll start a crazy feud with the neighbors. You don't hear about family feuds in the city, but they're a constant in small towns and can last generations.
I've lived in New Orleans, NYC, SF, and Tokyo, and other than New Orleans, I'd say every place has felt safer than when I lived in small towns or the country when I was growing up.
Most cities, especially nowadays, are quite safe. I think small towns are generally also safe, but from my personal experience, I've found the country to be less safe than cities because you're effectively on your own.
I think perhaps the city is safer for people who solve things by reporting problems to authority, whereas country is safer for those who rely on themselves. If you live in rural areas and depend on police for anything other than helping get the word out and possibly picking up someone after the fact, you are just fucked.
Edit: And in no time someone chimes in about their safe life they currently live in Tokyo, Japan -- probably the safest large city in in the entire world and one if if not the safest country in the world. Hope y'all have your visas ready. Of course we know this is in bad faith, because the Japanese analogy would be to compare Tokyo to rural Japan not to small town America.