Below is a chart, from University of Oxford economist Max Roser, showing a measure of income inequality called a Gini coefficient. Gini coefficients can run anywhere from zero to one. A value of zero would mean that income was distributed perfectly evenly among everyone in society; a value of one would mean that a single person has all the income and everyone else gets nothing. In other words, the higher the measure, the more unequal the income distribution.
The orange points show Gini coefficients for market income — that is, what people earn before the tax and transfer system comes into play.
The United States doesn’t exactly rank here as the most egalitarian advanced country on Earth, but we don’t totally embarrass ourselves. On pre-tax-and-transfer income inequality, we do about as well as France.
Now look at the blue points, which show Gini coefficients after considering tax and transfer spending, i.e., redistribution.
The United States does much, much worse. The only developed country with more unequal income distribution is Mexico. (Chile also is more unequal, though it’s not usually categorized as an advanced/developed economy.)
As I’ve said before, I favor using both pre-tax and post-tax policies to reduce inequality and help the poor. These data suggest there’s a whole lot more room for improvement on post-tax redistribution especially.