I frequently refer to the Independent Sector's definition of the differences between the three sectors: For Profit to pursue market opportunities; Public to provide that which satisfies the lowest common denominator of need (e.g. roads); and, Nonprofit to fill the void where For Profits have no incentive and the Public has no mandate.
There's a blog entry in the Christian Science Monitor that provides some helpful insight into the differences and the pluses/minuses of the three sectors using the future of the Fannie Mae and Freddie Mac housing investment organizations as a backdrop. Nonprofit Boards would do well to read this blog and consider what exactly their nonprofit really does bring to the universe (small "u" but maybe big "u" too). Thinking about the role of a nonprofit and its position in the community can be a helpful board exercise when revisiting theory of change and mission as well as making the case for the organization to funders and the public.