The National Review has an article by Jonathan Alder on the pros and cons of prizes compared to research grants and similar mechanisms for encouraging climate change mitigation technologies. The article comes down in favor of prizes:
Direct government subsidies are a particularly poor way to encourage innovation. Perhaps it should be possible to direct research and development funds toward the most promising and valuable technological endeavors, but this rarely happens in practice. Government subsidies tend to be dispersed on political criteria, rewarding large, politically connected incumbent firms, rather than innovative upstarts. Failing industrial dinosaurs with lobbyists on the payroll are in much better position to snatch up government goodies than revolutionary thinkers toiling in garages or private labs.
The article gives many examples of historical prizes from various fields, including space.
He does emphasize one serious problem with prizes, though:
The same characteristics that make innovation prizes so effective discourage their use by politicians. No one knows in advance who will win a prize, but subsidy programs allow government officials to dole out goodies to special interests and constituents. Subsidy payments go out whether or not a grant recipient delivers, or a problem is solved. Prize money, on the other hand, is only paid out if someone fulfills the preset conditions.
He phrases it in a way that makes it sound almost like an advantage, but as we're seeing with NASA Centennial Challenges funding, it makes it difficult to even start government incentive prizes. Congressional politicians have to look out for the whole country, but their job is also to look out for their direct constituents' interests, too, even if it means that local R&D programs that get funded might not be the most effective ones possible.
But if the climate-change problem is truly urgent, and federal policymakers wish to encourage the development of viable climate-friendly energy sources, they should phase out energy subsidies in favor of various prizes. The federal government should stop rewarding political influence, and instead encourage innovation by paying out for practical results.
For the reasons I stated above, this recommendation sounds completely impractical. Fortunately, it isn't an either-or situation. Moderate government prize programs can be funded without taking away anything significant from big R&D programs. The same is true in the space field - a well-run $10M or $15M per year NASA Centennial Challenges program could be extremely productive, but would hardly put a dent in the rest of NASA (~17B per year). Similar statements could be made for other space-related government agencies.
There are more comments on the article here.