This is an age old debate, and it's very hard to compare one vast continent to another. Regional differences between US cities and European cities are at least as large or larger than the difference between the avereages of US and European salaries/living standards etc. The difference between central manhattan and rural Apalachia is just like the difference between the fancy parts of Stockholm and rural eastern Europe. There is just no comparison in Salaries, Life expectancy etc.
When it comes to those of us that are "winning", the difference is there, especially for some professions like doctors who can basically make a killing in the US but not in Europe. That is probably to do with that it's an economic risk/investment to get the MD in the US, whereas in Europe it's normally free. When you are a finished doctor you aren't entitled to a fancy car - we just paid your MD so you better get to work and be thankful ;)
To make a fair comparison between me (a software dev) and a comparable person in the US (in a similar metro area of ~1M people) you'd have to make a pretty tricky calculation involving costs of healthcare, childcare, money saved for retirement, pensions etc. On the bottom line I think the US person would make a bit more money, but on the other hand would have a worse work/life balance.