Two big factors that are being grossly overlooked.
1.)Simply by virtue that the US has more people by several factors, looking at the numbers by per 100,000 it not apples to apples. The US is much, much more diverse.
2.)The US has more immigrants than the UK's entire population. We may even have more illegal aliens than the UK's entire population.
In reply to 1 - how else should you look at it?
Yes, there are more people in the US, but looking "per 100,000" (or maybe "per capita") is the only valid comparison.
Let's say a town of 100,000 has 1 crime - you can scale that to say a town of 1,000,000 can reasonably be expected to have 10. If the bigger town has 5, you can conclude that it's half as violent (or twice as safe) as the small town - or in another way that each individual is half as likely to be the victim of said crime.
If we were to just use raw numbers though (100k town 1 crime, 1m town 10 crimes) then the bigger town looks 10 times more violent.
By raw numbers, the US would look hundreds of times worse.
As for diversity, almost every country on the planet has a representative of some sort (diplomatic, legal or illegal) in the UK - so unless the stories of visitors from other worlds are true the US can't physically be more diverse (per capita, or by %, or by any other comparative measure).
As for 2 - there are 65-70 million people in the UK, the only figures I can find say that there are ~50 million immigrants in the US.
But that's raw numbers again - official stats (again, what I can find quickly) suggest that
14.4% of the US population are immigrants, with the UK lagging way behind with a mere
14.3% - illegals are shown to be around 3% in both places, within a couple of decimals again.
The figures for illegal immigrants have to be taken with some caution though, because until they're found you don't know they're there...
Here, the vast majority of illegal immigrants are only guilty of the crimes directly linked with their immigration status - stuff like border crossings, working without a visa, not paying tax - do they roam the streets in packs of marauding pillagers over there?
Legal immigrants and 'indigenous' people are responsible for a far greater number of real crimes, whichever recording method you choose.