In this case, it could be a combination of things.
1) No way to know what state your system is in, which is critical. The number of background processes, in particular. With a dual core CPU your system is going to load up faster, with fewer processes than a quad core would do.
2) What video resolution are you running the game at? The 960 is a decent video card, but will struggle with any resolution passed 1920x1080. The higher the resolution, the faster the video card is going to load up and slow down.
The DXDIAG output file might give some clues to help.
FOr AH3, the video card is the primary performance limiting device. The CPU is next.