From experience I'd say OpenGL is sometimes better than Direct3D, although the same applies the other way round ;)
Games like Quake 4 I believe use OpenGL which is more compatible with some GFX cards, as for your card I'm really not sure, I'm not all that familiar with different names and brands, I just buy what's more expensive and has better reviews, generally. Hence my top-of-the-range AGP card :D
To be perfectly honest, Quake 4 doesn't run as well as it could on my card, while games like HL2 run way smoother and look better. This may just be because it's not such a demanding game as Quake 4 is, but I do think the look of what can be produced by HL2's Source engine on D3D can look a lot more sleek than Q4.
But anyway, OpenGl has some different features to Direct3D, but recently Direct3D has been getting very slick and is generally a wider used platform for games these days. Here's an extract from an online comparison between the two:
"For a long time, Direct3D was considered to be pretty bad compared to OpenGL. Recent advancements in the API, however, have made it very powerful and stable. Many people now believe that Direct3D is the standard for graphics on Windows platforms, not OpenGL. Microsoft works very closely with graphics hardware companies to make sure that any new features that they introduce will be supported in Direct3D. Often, Direct3D supports features before cards do."
I'm not sure if that helps or not, but it's how I understand it to be.
