Maybe with the assault figues it's a case of more pub/
neighbour/whatever brawls get away with being assaults
whereas in the US they end up as murder rather than
assault statistics! :-) (I'm semi-joking here, please don't take
offence!)

Actually, you are really more or less right about this. The total amount of
violence in western nations is more or less the same no matter where you go.
But in the US, a gun is much more likely to be involved in a violent crime,
and gun injuries are simply more deadly. So while the combined rate of
murder and aggravated assault (i.e., grevious bodily harm in the UK) are
about the same in our two nations, the ratio between these two rates is very
unequal. More assaults result in death here in the US than is the case in
the UK.

Oh, and someone said New York was the worst place in
the US...I think it's long ceased to be that. I believe that title
now goes to Washington DC. According to the web page,
the murder rate in NY is 8.6 per 100,000, whereas in
Washington DC it's 49.15 per 100,000.

Every year, it's like a race between DC, New Orleans, and Detroit to see who
can come out on top.