Let's be clear: Clinton has no privatization plan. He has a stock investment plan (which I rather like for the reasons Milton F. hates it).
The other part of the plan is a supplemental private savings plan, the USA accounts, which are more analogous to IRAs than to Social Security. And from the details I have seen, they look a lot better for working class folks than IRAs.
IRAs are based on tax free savings, which benefit those who have high tax rates (ie. rich folks) a lot more than those who have low tax rates. Essentially, income taxes were cut for rich people with much less gain for working class folks.
By matching contributions with government money, the proposed USA accounts are essentially transferring money from the progressive income tax collection to working and middle class savers. The proposal I've seen says that something like $600 of saving would be matched with another $400 cash match by the government. That is direct transfer of wealth.
The biggest criticism of the USA accounts are that many poorer folks can't afford to save, so won't get the benefit, but since the savings needed ($600) is low, that is a lot less of a problem. The old IRA system meant that to get the equivalent of a $300 cut in taxes (useful only for those paying tax), a working class person in the 15% tax bracket had to save $2000- a much more burdensome approach for less benefits than the USA account.
The USA account is not perfect but it is a radical improvement over IRAs for helping working class folks save for retirement. Social Security is not enough for most people, so supplementary pensions are needed. We can fight to demand that businesses provide them (and even integrate USA accounts into them to encourage every worker to get one), but this does sound like a straight up improvement on what we have now with IRAs and 401Ks that benefit rich folks.
--Nathan