D3D is best used for Windows-based games. OpenGL is best used for cross-platform games and any other 3D application. Otherwise, they're pretty much the same thing.
If you want to do games, pick one - whichever you find easier.
If you want to do modeling / simulation applications, use OGL as few people use Windows for such applications (they use SGI workstations, in some cases Macs, and in a few instances linux boxes).
As far as OpenGL being best API for nVidia cards - I'm not sure. All I can say for sure is that nVidia has the best support for OpenGL on standard x86 machines.