The EU has always made substantial transfers from richer to poorer countries (though its budget is only about 1% of GDP.) Being in the EU has been pretty good for the Eastern European countries that joined, both purely financially and in securing their democracies, just as it was for Spain and Portugal which have made substantial progress in catching up with the likes of France and Italy since they joined in 1986.

Sadly the same can't be said for the single currency - which many Eastern European countries haven't yet joined. Greece is perhaps the main counterexample in that its GDP per capita is no higher compared to France than it was when it joined (its GDP dropped by a huge amount since the 2008 crisis.)

Imagine if something similar would have been possible in the Americas.