NIH grants are pretty good, but they have not kept up with inflation. ERC grants are better, unless you are in a country with particularly high salaries. NSF grants are not that special.

Europe spends more on academic research than the US, both in absolute terms and as a fraction of GDP. (The US spends more on R&D in general.) European academics are also less dependent on government funding. While European old money has long found it prestigious to fund arts and sciences, US donors are more likely to fund education or buildings.

European academics have continued to immigrate to the US, mostly because there is less competition for resources. It's easier to get a faculty position or a grant in the US, because you are competing against fewer people. Because academic jobs are worse in the US relative to the alternatives, fewer Americans are willing to pursue an academic career. That leaves opportunities for immigrants who have already chosen the academia and are willing relocate.