I lived in the US for a while and had the chance to make it permanent. I chose to return to the UK for a number of reasons but included in them was that I was at the beginning stages of an illness and knew that I would have much better employment rights in the UK than the US. Had I stayed permanently in the US, I could very well have found myself jobless because the economy was contracting at the time. Then I would have been screwed from a health care provision perspective. Healthcare is fantastic in the US if you have a job...not so great if you don't or are low paid (pre Obama care).
Typical holiday entitlements are far less than the U.K. standard of 28 days. And maternity leave provisions are far less too.
That all sounds negative to Americans reading this, but that was the choice I made based on facts at hand.
I go to various States in the US several times a year and do a lot of work with Americans. I have just done a quick count and I have visited 16 of the 50 states which is more than your average American. Guns never concerned me when I lived there, nor when I visit, and the food choices are wonderful, particularly seafood in places like Boston.
The American culture is insular and this worries most of the well educated Americans I know. I can understand the comment in the OP. There are enough immigrants from Mexico, Cuba and African countries who want to live there for Americans to get the view that everyone wants to live there. We might look to Calais and form the view that everyone wants to live in the UK. It depends through which lens you look at the question.
From a knowledge perspective even if the average Brit gets their news feed from the tabloids they are still much more knowledgeable about the world in general than the average American. I feel this most when I visit the US and switch on the tv news programmes or get the morning paper while a major world event is going on. In the UK and rest of Europe our tv channels and newspapers would be dominated by that world event but a lot of the time in the US, unless you're watching CNN, that event might largely be ignored by the mainstream channels such as abc, NBC or cbs.
I think if you're a white middle class family with employment then the US has a lot going for it and some of the issues I have mentioned don't resonate (healthcare isn't a problem, you can afford better schooling, and you're likely to be in the 50% of Americans that have passports and use them). Particularly so, if you're on mumsnet. However if you're not in that demographic then some of the things I mentioned matter.
If you're a young black man in the us, you face a racism in your day to day life, same as in the uk. You're far more likely to be subject to stop and search in the UK. But other than the odd case in the UK, stop and search by the police is where it ends. In the US, a young black mans far bigger legitimate concern with the police is that it might be stop and kill rather than stop and search. That's why #Blacklivesmatter has resonated a lot more in the US than in the UK.
On the other hand, in the land of the free, I always meet more immigrants who have done well in the US than their compatriots in the UK.
On a more positive ending note, the fall/season with the celebration of Halloween, Thanksgiving and Christmas is absolutely fantastic and nothing beats pumpkin pie!
I have travelled all over the world, about 40 countries at the last count but one trip I would love to do is a drive across the US.