That's unlikely due to extremely high taxes in the EU for individuals. People who know their stuff tend to migrate where they get more in return for their talents.
Taxes actually come out about the same when you add the multitude of separate tax systems in the US (federal income, social security/medicare, state, local), and then in the US additionally have to pay extra for things that are paid by taxes in Europe, health care being the biggest such expense.
And then there is the expectation of working 24/7, nobody has much vacation and nobody takes what they get, etc etc etc. Yeah, quality of life for Americans is nowhere comparable to Europeans, unless you're in the "I no longer work for money, my money works for money" set.
Frankly, I don't see the point of celebrating the fact that my money is going to private companies as premiums/co-payments rather than to the central government as taxes, while getting worse medical outcomes for it (with a risk of medical bankruptcy).