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I think it is true that the US has higher murder rates, but it is also true that a number of modern countries now have higher overall violent crime rates than the USA.

I recall recently reading, too, that London and Toronto now have higher street crime incidence rates than does New York City (or that may be their respective overall violent crime rates; I don't recall precisely. Sorry it's late, and I'm not apt to go look it up all over again, as I read it some weeks or months ago; but it should easily searchable on the web if you're interested).