Yay thread pension!
Personally I prefer OpenGL from an idealistic point of view, but realistically for the windows gamer DirectX is better.
OpenGL does things right, but the time it takes for the right way for a new technique to be nailed down severely counts against it. DirectX is able to quickly provide an implementation so the turn around for new techniques to get into games is faster.
Of course, then you've got the arguement about what leads what, in terms of hardware and software and we seem to be stalled on DirectX9 for quite a while with not that many new features coming out on graphics cards. I think that's a good thing because changing hardware and software capabilities must be one of the biggest drawbacks to development for the PC compared to consoles.
I've only programmed for linux/unix, and there obviously openGL is a godsend. It's also IMO quite easy to use, and 'makes sense'. I suspect DirectX is better for plug and play type effects which can be built into game development tools, so it's possibly a quicker API to program for as well.