10
Performance-wise, and assuming decent GPU drivers, there is no difference overall.
Some operations are inherently faster in OpenGL than in DirectX9, although DX10 remedied that.
But a good rule of thumb when working with external hardware is that it's not the API you're using that determines performance.
When writing network code, the bottleneck is the network adapter, and it doesn't matter if your socket code is written in .NET, plain Berkeley sockets in C, or perhaps using some Python library.
When writing code to use the GPU, the GPU is the limiting factor. The biggest difference between DirectX and OpenGL is that one might require a function call or two more than the other to achieve certain tasks -- and the performance cost of that is pretty much nonexistent. What happens on the GPU is the same in either case, because that's determined by your GPU driver, and because both OpenGL and DirectX try to be as efficient as possible.
There are valid reasons to prefer either API though.
DirectX has much better tool support. Microsoft does an extremely good job of that. Debugging and optimizing DirectX code is much easier with tools such as PIX. And Microsoft also provides the helper library D3DX which provides efficient implementations of a lot of commonly used functionality.
OpenGL has the advantage that it's not tied to a specific OS. DirectX9 only works on Windows. DX10 and above only works on Vista and above.
OpenGL works on any OS where an OpenGL driver has been written.
On Windows, the situation is sometimes a bit awkward though. Windows itself only comes with ancient implementations of OpenGL. (XP with v1.1, I believe, and Vista/7 with 1.5).
So OpenGL apps on Windows rely on the GPU vendor to provide an updated implementation with their drivers. ATI and NVidia do provide very good implementations, so it's not that much of a problem. Intel's OpenGL drivers are generally la
It would generally be about the same. There was a time that DirectX had a distinct speed advantage over OpenGL, but for most practical purposes, that's ancient history.