Livia, thanks for the note. I suppose it depends on how you do it and what you are comparing to. You listed 3 of the most expensive cities in the US, similar to London, Paris, and Zurich. Life in Texas, where I am from is about half of what it is in LA. Life in rural America is significantly cheaper than even life in a place like Houston. If you are willing to live in a small town, you can certainly live very cheaply in the US.
Also, if you want the “American” lifestyle of owning a big house, two cars, etc. it is certainly more expensive in Europe. According to Numbeo.com, while rents are cheaper, Barcelona house purchase prices (flats, actually, villas are surely even worse) are about TWICE Houston. Don’t forget taxes are lower in the US, gasoline is cheaper (about half), cars are cheaper, etc.
Probably for a more “European” lifestyle of renting a small apartment, public transportation, etc. you can live cheaper in some places in Europe like Spain and Portugal. But overall, life in Europe is more expensive for the same living arrangements.
I’m not saying the US is better by any means, and I’ve lived in both. But it is important to compare apples to apples.