The issue with most of the studies that say this is how they measure mobility. If the focus is on the ability to move up in income percentiles, then it's an unfair comparison.
Why? Because while it sounds nice to say "avg german child moves from top 50% to top 65% while avg american only moves from top 50% to top 55%", American salaries are much higher, and cost of housing is on par or lower than Europe, so top 55% is a much higher financial increase for the American.
Now that you say it, I see a lot of these comparisons talking about odds of a person born in one quartile/quintile ending up in a different bucket as an adult. Often, it's specifically cited as the chance of a person moving between the highest and lowest buckets. Which on reflection is actually a composite measure of income variability, inequality, and societal wealth.
Running those stats alongside a Gini coefficient would help somewhat, since lower coefficients imply more similar gaps between adjacent buckets. But even that's not enough on several levels. It wouldn't distinguish where inequality falls, particularly patterns like the US and Singapore with large variation inside the outer buckets, so a Lorenz curve would be more useful. It also doesn't clarify the raw size of the changes - position in society matters, but it also matters whether a ten-percentile jump is a 10% gain in purchasing power or a 100% gain.
I'm a bit embarrassed, really. That's a massive gap in the utility of those stats, and I never even considered how many different things the same numbers could mean.
It's something I didn't realize until recently myself. There are several things Europe does better than the US in, but earning power is not one of them.
Why? Because while it sounds nice to say "avg german child moves from top 50% to top 65% while avg american only moves from top 50% to top 55%", American salaries are much higher, and cost of housing is on par or lower than Europe, so top 55% is a much higher financial increase for the American.