Syntactically I prefer OpenGL over Direct3D any day - if you're a Windows programmer you may be able to read things like "hRes=lpddClipper->lpVtbl->SetHWnd(lpddClipper,0,hwnd)" or "hRes=lpddPrimary->lpVtbl->Blt(lpddPrimary,&rDstRect,lpddDevice,&rSrcRect,DDBLT_WAIT,NULL)", but it just makes my head hurt.
It's reasonably fair to say that OpenGL had beun to fall behind Direct3D in terms of features and usability, but the aforementioned version 2.0 of OpenGL is set to bring OpenGL right to the forefront yet again.
There are a number of OpenGL bindings for Java, the popular one around here being LWJGL. In fact, the responses you've had so far have been from LWJGL developers, but they forgot to mention that...
Yes, OpenGL works on Windows - very fast in fact. It's no big secret that Quake 2 and 3 and the new Doom3 are all written primarily in OpenGL. With games like that using it, you can bet that commercial graphics card drivers are very well optimised for OpenGL.
Interesting question about whether it's going to be replaced by the "next big thing"... does anyone know of any 3D interfaces in general use apart from OpenGL and Direct3D? Are we really in a two-horse race here?