After I posted my original piece, I was off the web and didn't see the comments from others, but I think David answered them pretty well.
I would add one thought. A contest doesn't guarantee that the resulting innovation won't be patented, so if the sponsor patents it, the price to society may be a lot higher than just the prize money. Thus, I may have exaggerated the relative merits of contests and patents or copyrights. But I remain intrigued.
I was led back to this subject by a post from Alex Tabarrok (link here) which takes you to a Business Week story about Goldcorp. The gold mining company was in trouble and had suspended mining. It had mining leases. Question: should it develop any of them and if so how. In a contest, it posted the geological data on the leases and issued the "Goldcorp Challenge" which made a total of $575,000 in prize money available to participants who submitted the best methods and estimates. Big response and big success for Goldcorp, though rising gold prices had something to do with it as well.
Subsequently, I Googled "contests+innovations" and got 915,000 hits. Obviously, I haven't looked at more that a few, but there seems to be more going on out there than I thought; lots of competition, just not from patent and copyright holders.