I'm having trouble finding a more recent source, but as of 2012 that wasn't close to true. It's actually a larger gap than I expected. I'm going to keep researching to see if I can find more recent numbers. Do you happen to have a more recent source?

https://en.wikipedia.org/wiki/List_of_countries_by_net_migra...

__EU__

Total net migration: 2,324,066

Net migration per 1000 inhabitants: 4.60

__US__

Total net migration: 5,007,887

Net migration per 1000 inhabitants: 15.94