Not all private schools are the same. . .and private schools do NOT outperform public schools when all factors are held constant:

http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2006461

But poverty is incredibly powerful:

http://www.jrf.org.uk/knowledge/findings/socialpolicy/2123.asp

"Living well's the best revenge." r.e.m.