After taking care of 'the platform', the 3D-card is the only thing left. The 'fill rate' describes the amount of pixels that a 3D-solution can render in a given amount of time. We all know that a frame consists of a certain amount of little dots, called 'pixels'. Each screen resolution requires a certain amount of pixels. The common resolution 640x480 is made of 307,200 pixels, while a high resolution as 1600x1200 requires 1,920,000 pixels. The 3D-chip has to 'render' each pixel of a frame before the frame can get displayed. The 'frame rate' is defined as the number of frames that can be displayed in a certain amount of time. It's easy to see that it requires a lot more rendering performance to supply a certain frame rate at a high resolution than at a low resolution. This is why typically 3D cards score high frame rates at 640x480 and lower frame rates at 1600x1200. After all the 3D-chip has to render more than 6 times as many pixels for each frame at 1600x1200 than at 640x480.
Nowadays 3D-chips have several rendering pipelines that can operate in parallel. Such a pipeline is usually able to render one pixel per clock cycle. Thus the maximal pixel fill rate is the 3D-chip clock times the number of rendering pipelines times the number of chips in case that more than one 3D-chip is being used on a 3D-card. A typical example would be NVIDIA's new GeForce2 GTS chip, which is clocked at 200 MHz and which comes with 4 rendering pipelines. 4 pixels x 200 million/s = 800 million pixel/s. 3dfx's Voodoo5 5500 is clocked at 166 MHz, each chip has two rendering units and the card comes with two chips. 2 pixels x 166 million/s x 2 = 667 million pixel/s.
Now without taking in consideration triangle size, T&L and hidden surface removal one can still say that if the fill rate remains constant frame rate will go down as the resolution goes up. Ideally, you find the highest frame rate at the lowest resolution and see it coming down continuously as resolution increases.