The median full-time wage in the US is 70% higher than the EU median full-time wage.
The high US inequality is a result of the spectacularly extreme outcomes that come from simultaneously having a very large integrated economy & population base, extremely high economic output, and extreme national wealth.
If you integrated large parts Europe, you'd see a similar extreme inequality between eg the top end of Norway or Sweden, and the bottom of Bulgaria or Moldova. Or othewise the top end of wealth outcomes, such as Amancio Ortega or Bernard Arnault, versus the bottom end of wealth outcomes in Croatia. Except the US bottom is dramatically above the bottom of Europe.