those who would benefit from migrating to Europe cannot afford to, are greatly discouraged or straight up can't (passport, language barriers etc)
OTOH most of those going to the US right now are from eastern Europe, following the flood after the wall fell.
Or people who are going there to increase their salary, not necessarily their quality of life. I have several friends who are working for one of the FAANGS in the US but come back to Italy for medical check-ups or holidays because here's cheaper, safer and it's a better place to spend your free time or raise kids.
European population in the US is pretty stable though.
In the end people of European descent are still the largest ethnic group in the US of A, the USA were founded mostly by anglo-germans while the opposite has never been true.
An European citizen can go to Egypt or Estonia or the Canary Islands or Iceland or Norway or Switzerland without a passport
OTOH it's easier to learn English for an European - we all study it in primary schools - and go to the US than for an American to learn Norwegian and move to Norway.
It's also a lot less of a cultural shock to go EU->USA than the other way around.
Any source? I doubt many EU citizen would agree with that, especially those aware of US work and health system.
But plenty of them find it hard to fit in socially, and then leave later.
I think it's less the money aspect, and more the fact that American society is more bland, uniform. It's easier to fit in. In Europe, unless it's a true international metro (amsterdam, london, brussels, ...), there's a huge cultural barrier. You just can't hitch into it as an adult. Your children will fit in, but not you.