DirectX is Microsoft's whiny answer to not getting what it wants out of OpenGL. DirectX is a more CPU intensive, slower overall API than OpenGL.
To illustrate the point - drawing a cubemap in DirectX takes about 15 lines of code whereas in OpenGL it only takes about 4. Any student of 3D programming will tell you that using OpenGL is vastly superior to DirectX.
Really, the only thing DX has in its favor is that its development has come along faster than OGL. I suppose that's what comes from Microsoft being autonomous for controlling DirectX. But if there ever is an option to use OpenGL in a game you can bet your bottom dollar that I'm going to use it.