This is an interesting video and it's true enough. Not unbiased but true as far as it goes. The US has more than 5 times the population and 40 times the land (just in the lower 48 states).
If you want to live downtown in a major city with good public transit and walkability, you can accommodate another 65 million people (UK) there.
If you want low crime, don't live in Memphis or Louisiana and the average rates come way down. Even in a nice major city but with a little higher crime you just choose not to live downtown and pick your neighborhoods.
Whether I was young and money was tighter or now when it's not, I've never lived in a higher crime area, by choice. It's easy.
Most of the living standards mentioned in the video weren't material living standards, they were social in nature. Being obese is a choice and not a "living standard". Health care results in the US are good. Just don't do drugs, be in a gang or drive reckless between 18 and 45 and your stats are fine.
There isn't the dense public transportation in the US (outside of the NE) that exists in the UK because the density levels are completely different. In the western half of the country, 10% of the US population lives in a strip along the coast and 40% of the country has only 10% of the total population. Of course there isn't a lot of public transportation. I'm guessing in Australia, Hobart and Alice Springs don't have a lot of subway and public transportation either, just like of the western US and for the same reasons. There are buses but you generally aren't going to be doing without a car.
Again, all you can really say if that if you grow up the the UK you may prefer that system and if you grow up in the US you may prefer that system.