I went from London to NYC, from NYC to Stamford (CT), and from Stamford back to London. And a lot of commuting between the 3.
From London to New York
Didn't notice much difference. Public transport was equally bad, it was equally busy. Money talks. Landlords suck. Flats or houses are expensive.
Where in London it was common to go outside during lunchtime to 100s of food stalls, it was not so common back in NY.
Restaurants, both good. Supermarket stuff, enough choice. Whether I would cook at home in the US, or the UK, I was so bad, preparing a steak would mean it’s probably alive at the end of it. So we've seen plenty of restaurants. Tips are noticeable different in the US/EU, but you get used to that quickly.
And let’s be honest, you either come to these cities as a 4-day tourist or to churn and burn ridiculous work hours, not to “live the life of averageguy.” City full of workers. Always busy. Berlin or Paris isn't different.
A notable difference (UK/US) is perhaps nightlife, it closes earlier in the UK. And whatever the weather, girls often dress the same in the UK, lot of leg exposure (not always a benefit). It has more elegance in the US, and really speaks a far stronger 24/7 attitude than the UK.
It felt like going from London to a small European city. It didn't feel American at all.
I think its very possible not to notice much differences at all in North America versus Western European cities.
Stamford, were it not for the lack of jobs, could easily be a place I could retire (as former banker) and live the rest of my life. And that particular life would not be much different as a big city in the Netherlands or Germany.
Difference West/East Europe is far bigger. I also lived in the Netherlands, Germany, Poland, differences started to become bigger when moving more and more east. Technically, a compare Europe versus US is an impossible answer as you'll get 1000s of opposing views but I would much rather stay in London ❤️.