When I say better off, I'm talking about quality of life, not money. Surely many of the American poor would want to live in Sweden if they knew how high the quality of life is for low-income earners in comparison to theirs -- but because they are poor they have very little chance of ever getting emigrating to Europe.
Conversely, someone who's fairly successful in Sweden might realize that they could be earning much more money in the United States--because of the income inequality--and thus might want to emigrate to the U.S. Chances are they'd have a much better chance of getting there, too.
I live in the U.S., but grew up in Europe. If I didn't have skills that were highly sought after, I wouldn't want to live here. (FWIW, the bigger reason I do live here is that I have immediate family in the states.) I'll bet you that's the case for most people emigrating here from Western Europe.