I am a Java programmer who has a fair amount of experience with Swing, which I have used for 2D game programming. I am interested writing 3D games and am not sure which API to use - OpenGL or Direct3D.
Both offer excellent performance if used properly. I don't think it is possible to prove that either is faster than the other.
Of course, OpenGL has much wider compatibility across platforms, but if all you care about is Windows, then that is not an issue.
Direct3D is somewhat more object-oriented than OpenGL; it's a COM API while OpenGL is a C API. Neither leads to pretty code, they're very low-level APIs after all. If object-oriented and clean is what you want, you should look into some higher-level utility than these APIs, for instance XNA/MonoGame.