For example, it seems to me the absolute income version would be steeper at low incomes, perhaps amplifying the perceived impact of things like a living wage or basic income on educational outcomes. (I'm talking mainly about the psychological impact of the curve's shape, not raw statistical truths.)
I felt strongly about this the moment I read the article on NYTimes - I reproduced the data set to the best extent I could and actually went about plotting against absolute income:
https://docs.google.com/spreadsheets/d/1jD87QN3pPZjoefrAm4E_...
That's a far more intuitive chart, that a lot of us will understand better. I also graphed how much these children actually go on to earn against absolute income. I compared these results in a blog post - http://unside.t4you.in/data/intuitive-axes/
HTH.