Unlike the overall negative tone of this study, I feel like poor kids actually have an advantage because they have a natural instinct to try harder to survive. Of course, there will always be those who simply give up because they think their station in life is set. It's probably more likely society and culture that keeps them down, not brain development.
On the other, rich kids have a skewed sense of need versus want, as well as effort versus reward. If everything comes easy, I'd argue rich kids are more developmentally challenged, possess less problem solving skills—especially under pressure—less able to deal with failure and less creative. Hence the "spoiled rich kid" stereotype. Whereas society constantly reminds poor kids all the things they can't do, rich kids are constantly reminded that they can do anything they want. Even well-meaning efforts like the "privilege" comic strip a while back reinforces this meme. I think that's where the real advantage comes from, and why the rich stay rich and the poor stay poor.
This is something very top of mind right now as I start to plan to have kids.