It seems there are roughly equal numbers of Europeans wanting to live in the US, and USians wanting to live in Europe. I imagine it being possible (albeit hard) to set up some kind of exchange system.
I think it would work out ok. There are plenty of wealthy Americans who would flock to Italy, for instance, if it were easier. And plenty of Europeans who might give a job in the US a whirl and then go home. And plenty of Americans who would love to spend a year working in Europe. And vice versa.
I don't think you'd see big imbalances between areas with roughly equivalent living standards.
But then, is 1 equal to the other?