Essentiallly. But the difference is not significant, DX10 just has a few more interesting ways of doing lighting effects (as I understand it, I could be wrong about this. This might have even changed now, with newer revisions of OpenGL being released).
For all intents and purposes they're the same, and can do the same things, except that OpenGL is not as integrated as DIrectX is. OpenGL handles only the sending on primitives to the graphics card, DirectX handles a bunch of stuff like model loading, texture loading, stuff like that. However, you can get a 3rd party library with OpenGL and not do that stuff anyway.
So I'd recommend OpenGL over DirectX, just because of it's portability.
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