OpenGL is infinitely better. Well not really but being cross platform, open source and being as powerful as or more powerful as DirectX. Not to mention that Microsoft copies the technologies in OpenGL then publicly slanders them. I would vote OpenGL.
Microsoft doesn't encourage competition of technologies to keep them from being stagnant and unreasonable. You use DirectX on Microsoft terms and not your own.
So game programmers out there
This is not only a subject of "game programmers" but also anyone in computer science specifically computer graphics. Just nitpicking details here thought.