I know that the Athlon II X2 isn't the best dual core, but it was still powerful enough to run the Dolphin GameCube emulator at full speed, something very intensive that's only optimized for two cores. Mine was 3.2 GHz, essentially as fast as a Phenom II X2 without the L3 cache. On most PC titles, one core would be fully loaded, and the other would be more than halfway loaded. And I'd get a horrible framerate. While a Phenom II X2 or Core 2 Duo would have probably been "better", it wouldn't have been enough to pull my framerate completely out of the gutter.
What's the new CPU you've got? Still, go in the bios and disable 2 of your cores. I can't see any difference in BF3.