Toonces is mostly right here.
What you decide to use depends on many factors...
What version of DirectX do you have installed, and does your video-card driver have good support for the newest version of DirectX? (DirectX updates mean new updates for Direct3D -- at least Operating-System wise)
What kind of support does your game have? Usually a game will support either/or. Cross-platform games are usually optimized for OpenGL, since it is an API that is platform-independant. Quake3 is a good example, being playable on Windows, MAC, and Linux. Games that are primarily Windows-based are usually optimized for Direct3D, so I'd use this driver when playing that game.
Now, if you're using CAD, OpenGL is the language that CAD apps are going to use. CAD is the reason why we have OpenGL. Direct3D is a newer API, but it is becoming very strong.
As long as you keep your drivers current, DirectX updated, and your games patched, there is negligible difference in performance for those few games that support both APIs.
Hope this helps.
Joshua Van Berkum