Arthur Diamond offers this abstract:
Regression analysis is used to test the effects of funding source (and of various control variables) on the importance of the article, as measured by the number of citations that the article receives. Funding source is measured by the number of prizes and the number of government grants mentioned in the acknowledgements section. The importance of an article is measured by an "early" count of citations…and a "late" count. Using either measure of article importance, the evidence suggests that private funders are more successful than the government at identifying important research.
This paper is worth a look, but I have some worries. First, private funding may have a better chance of picking the "cream" of private researchers, but without helping them much. Second, if you are famous it is easier to run up your number of private funders than to run up your number of government funders. Third, even most cited research has no real impact. We should be concerned with the extremes of the distribution, not mean citations. Fourth, private foundations may take greater care to seek out measurable outputs. Whether this helps or harms the quest for the extreme successes is hard to say.
A separate question is not which form of science funding is better, but rather how the two can best fit together. I put this and related questions into the "grossly underexplored but extremely important" category.
Addendum: Jonathan van Parys recommends this paper on the topic; the abstract is right on the mark and the authors are excellent.