Natália P. Monteiro and Odd Rune Straume have a new working paper, "Are cooperatives more productive than investor-owned firms? Cross-industry evidence from Portugal".
And the answer is that cooperatives are less productive than investor-owned firms.
The abstract reads:
We analyse empirically whether cooperatives and investor-owned firms differ in terms of productive efficiency. Using rich Portuguese panel data covering a wide range of industries, we apply two different empirical approaches to estimate potential differences in total factor productivity between the two groups of firms. The results from our benchmark random-effects model show that cooperatives are significantly less productive, on average, than investor-owned firms. This conclusion is to a large extent confirmed by the results from System-GMM estimations. The lower productivity of cooperatives applies to a wide spectrum of industries. In six out of thirteen industries, cooperatives are outperformed by investor-owned firms in all empirical specifications considered, while there is no industry in which cooperatives are consistently found to be the more productive type of firm.Of course it has been argued that an investor-owned firm is a particular type of producer cooperative; a capital (or lenders’) cooperative.
In their analysis Monteiro and Straume combine all forms of cooperatives but the basic results don't change when they look at particular types of cooperatives within a given industry. That is, productive efficiency of cooperatives versus investor-owned firms is not particularly related to cooperative type.