Robert Schiller, author of Irrational Exuberance has performed a study showing what would have happened with private accounts had they been in place every year since 1871. Under his examination, the private accounts proposed by George Bush (though still not in any official form) would lose people money 31% of the time. And 71% of the time folks would be better off under the benefits of Social Security. Keep in mind also that the U.S. stock market (and the U.S. economy) has done better than any other market in the world during this period. It's not likely that we'll continue to be doing quite so well in relation to the rest of the world.
The paper can be found on his web site.