OpenGL vs. Direct3D?

sl3xd asks: "When it comes to 3D graphics, there are two main competitors in the 'Mainstream' computer world: OpenGL, and Direct3D. However, aside from the fact that OpenGL is cross-platform, and has an extension mechanism, in what ways is it different than Direct3D? How does each handle the interfaces between the OS and the hardware? What are the rendering advantages/disadvantages to each? Do they use similar mechanisms - are they somewhat similar to program for? What are the advantages of Direct3D over OpenGL, and vice-versa?" Are there other 3D graphic libraries out there that can complete with OGL and D3D that sl3xd might have missed?