The SOE Act states that SOEs, basically, have to be run like normal non-government owned firms. In effect this requirement is the same as you could get if private owners have a stake in a firm. The private owners would, we assume, wish to maximise profits, but the government may not. And you see this with SOEs. The government often wishes to intervene in the running of SOEs to get them to carry out non-profit maximising activities, just as it would if it had a partial stake in a mixed ownership firm.
This problem of having SOEs (or mixed ownership firms) trying to serve two masters was noted more than 10 years ago by Spicer, Emanuel and Powell in their book "Transforming Government Enterprises: Managing Radical Organisational Change in Deregulated Environments" (The Centre for Independent Studies, 1996). They warned that there are two pressures on SOE's: the first being towards privatisation since the productivity and efficiency gains achieved by SOE are in danger of being eroded over time. Privatisation is a way of both cementing in the commercial orientation of enterprises and wringing out further gains resulting from the high powered incentive and control mechanisms which can be bought to bear in privately owned and publicly traded companies. The second pressure on SOEs is towards being pulled back into the public sector where social and political objectives can be more readily be meet. Most interventions seem to be more politically motivated. You can't have your cake and eat it. Either the firm (SOE) has to set out to maximise profits or it has to try to carryout some political or social role, what it can't do is both. The two objectives just conflict.
These pressures would also be there for a mixed ownership firms and help explain why they don't do as well as fully privately owned firms. For example, Aidan Vinning and Anthony Boardman in "Ownership and Performance in Competitive Environments: A Comparison of the Performance of Private, Mixed, and State-Owned Enterprises", Journal of Law and Economics, vol. XXXII (April 1989) conclude
'The results provide evidence that after controlling for a wide variety of factors, large industrial MEs [mixed enterprises] and SOEs perform substantially worse than similar PCs [private corporations].Well now the Americans have gone one better (or worse). The Obama administration’s plan to restructure Chrysler involves the company having three different sets of "owners": Fiat (35 percent), UAW (United Autoworkers) retirees (55 percent), and the U.S and Canadian governments (10 percent collectively). As William F. Shughart writes
Reconciling their separate and divergent objectives may well be impossible. Fiat will want profitability, the union will want to protect pensions and healthcare benefits, and governments will want to protect jobs and pursue who knows what other political ends—tellingly, the administration’s first priority is to preserve UAW jobs.And how long will it be before the U.S. and Canadian governments differ as to what the firm should be doing?
The upshot of this is, don't bet on seeing a robust, well run and profitable company anytime soon.