OpenGL vs. DirectX?

Depends on what your goals are. OpenGL gives you cross-platformness for free, and it exposes advanced card features through extensions; DirectX, by contrast, is a Microsoft thing and you have to wait for a new version to get new features.

You know all that "DirectX10 features only work under Vista" thing? It's crap. DX10 may only work under Vista, but OpenGL 2.1 exposes all the same features under any system you like, if they're available on the card.

In short: If you want to code to a fixed set of capabilities and aren't too concerned with portability, use DX. If you want portability and don't mind writing several different versions of various functions (from complex to simple, the best one is selected at runtime based on card capabilities), then go with OpenGL.

OpenGL 3 is on the horizon, and it's going to be object-oriented, which will be a big plus. The spec was supposed to be out by now, but there's been no word so far. It'll be awhile before drivers arrive anyway, so just assume you're working with 2.1.