Currently speaking, ATI has superior DX9 PS2.0 support and can run them easier as thats how the current DX9 cards from ATI were designed for.
Nvidia, starting with the NV30 (fx5800) tried to start their own code revolution with Cg and their design was not up to the MS DX9 spec as much as it was up to their own spec. In other words, Nvidia took the wrong path and ATI stayed on the DX9 spec to the letter. So, if you own any nvidia gpu from NV30 to NV38, you will have inferior DX9 performance (speedwise). NV3x can do PS 2.0 so you will still have the quality, but it just can't do it as fast as ATI at the current stage of the game.
As for OpenGL, the roles reverse. From the original GeForce and maybe even before up til current nv38, Nvidia has dominated OpenGL performance. NV cards are just made to run it better and more efficeintly just like ATI is made to run the DX9 codepath more efficeintly.
You have a 5700U and you will be blazing through Doom III without a hitch. You should also be fine to play HL2 although it will not play as fast as ATI cards that exist now. We wont know about the next gen cards officially for a few months yet. Who knows what will change by then.
Hope this helps ya.
Keys