How does faster video memory effects performance?

I understand that with faster VRAM you get more bandwidth for the GPU, but I'm trying to understand how that effects the GPU's performance with different game settings.

Comparing my 9800XT (256bit memory bus) and Mobility HD 2600 (128bit) in Half Life 2: Episode 2 (both with everything high execpt medium shadows), I found that eventhough the 9800XT has more bandwidth, I have to run at 1024x768 with 2xAA because the 9800's shaders cannot make use of the bandwidth as they're struggling to do all the image processing. But the HD 2600 can run at 1280x800 0xAA with HDR (HDR cripples the 9800XT, but AA cripples the HD 2600).

So more bandwidth isn't useful if you GPU's shaders can't cope at high enough resolutions to make use of the extra bandwidth. But this is going to change a lot with different games. So playing a game like Bioshock on my DDR2 HD 2600 at 1024x768 with all the image processing on (shader, shadows & post processing) is going to bottleneck the GPU core & shaders, so more bandwidth for higher resolutions (higher resolution increases texture size) wouldn't help because the GPU core can't cope with doing more shading to the increased amount of pixels on screen at higher resolutions. So to make use of more bandwidth from DDR3 I'd have to lower the shader detail.

Am I thinking along the right lines?