Even on a per-capita basis, the US has considerably higher levels of both legal ...

Even on a per-capita basis, the US has considerably higher levels of both legal and illegal immigration.

About 3% of the US population is in the US illegally compared to about 1% in the EU.

Overall, about 15.8% of the US population are foreign born, compared to 6.1% of the EU.

Just like in the US, immigrants aren’t evenly distributed though so some countries have far higher percentages - just as some US states do.

From the chart I linked it seems clear to me that the US doesn't have high new immigration numbers anymore relative to its population.