>Net migration to the US from the richer EU countries is about 0, i.e. about the same number of US citizens are moving into the EU as are moving from those EU countries into the US.
Not true. 10-17% of Canadian, British, Australian, and Swiss scientists move to the US. (https://np.reddit.com/r/dataisbeautiful/comments/37lgxg/the_...) These are percentages of all researchers, whether they emigrate anywhere or not. (By contrast, only 5% of US scientists leave theiir country.)
Among the general population, there are 824,000 Britons living in the US, compared to 159,000 Americans living in Britain. Given that the US's population is about five times that of Britain's, that means that on a per-capita basis a Briton is 25 times more likely to move to the US than an American is to move to Britain.
Of course fewer Europeans migrate to the US than in the 19th and early 20th centuries, or compared to Latin American countries today, but they still come and the net flows are still considerably in the US's favor. There are 1.2 million German-born people living in the US, for example, versus only 150,000 American-born people living in Germany, although the US has four times Germany's population. Sweden and Norway? 15,000 Americans in each, compared to 54,000 Swedes and 36,000 Norwegians in the US. Sweden has 10 million people—the size of Los Angeles County—so there would have to be 1.62 million Americans living there to match those going the other way on a per-capita basis. There are 49,000 Swiss born in the US, compared to 24,000 American born in Switzerland. The US's population is about 37 times larger, so a Swiss is 75 times more likely to move to the US than the other way around. There are 71,000 people born in Austria living in the US compared to 7,700 Americans in Austria, implying that an Austrian is more than 300 times (!) more likely to move to the US.
Same with non-European countries; for example, 945,000 Canadians in the US versus 279,000 Americans in Canada. Since the US's population is nine times that of Canada's, on a per-capita basis a Canadian is 27 times more likely to move to the US than the other way around. Yes, the US has a nicer climate than Canada, but this is consistent with other Anglosphere countries; 75,000 Australians and 26,000 New Zealanders are in the US compared to 54,000 Americans in Australia and 13,000 in New Zealand, respectively, so on a per-capita basis Australians are about 20 times more likely to move to the US and New Zealanders an amazing 140 times. Etc., etc.
(All data comes from Migration DRC (http://www.migrationdrc.org/research/typesofmigration/global... see table 4. Military forces are excluded. A less-detailed graphical version (http://migrationsmap.net/#/USA/arrivals) is also available.)