If you bring it down to numbers, the pay is definitely higher in the US. For instance, an average software engineer out of school can expect a starting salary between 25 and 35k euros on average in France. In SF, it's more $70-90k at the very least.
But then you have to account for the higher cost of living, transportation (even if you don't drive, French employers pay for a part of your public transportation tickets), and all the other perks that are inherent to your job (insurance, subsidized lunches,...) and inherent to the country (better public education, etc.).
So I think it's hard to say empirically that engineers are better off in one country rather than the other- although I'd be tempted to say that very high end engineers are better off in the US rather than Europe, and the average engineer is better off in Europe rather than the US.
But then you have to account for the higher cost of living, transportation (even if you don't drive, French employers pay for a part of your public transportation tickets), and all the other perks that are inherent to your job (insurance, subsidized lunches,...) and inherent to the country (better public education, etc.).
So I think it's hard to say empirically that engineers are better off in one country rather than the other- although I'd be tempted to say that very high end engineers are better off in the US rather than Europe, and the average engineer is better off in Europe rather than the US.