what program would you use for DirectX 11?
Ok well what language are you going to be using to program graphics? If it is c/c++ then I would have to recommend OpenGL because honestly they are driving DirectX into the ground. Now really this is a kind of unfair comparison considering DirectX is a full graphics, sound, input, etc API and OpenGL is only graphics. Now if you are looking for graphics, I will still have to say OpenGL because it is also cross platform.