I suspect your friend's 4-core at 4 GHz, unless it's also an FX branded model, is actually going to be more consistent in getting work done than your FX-6300. While your FX-6300 can turbo up to 4.1, which would at least match in a reasonable fashion the work output from a Phenom-II at 4 GHz, your chip is not designed to run at that speed under full load, so is likely never going to match your friend's clock speed consistently, unless you do some manual tuning / overclocking. If the two chips have similar IPC at the same frequency, you need to match the speed of his chip to be on par. You can't expect the turbo speeds to make up the difference reliably.
Your graphics card may be better on paper, but sometimes that doesn't matter. Try playing Rage with an AMD card, or using TressFX on an NVIDIA card and you may see my point. If your friend is very nice, he might lend you his graphics card to test in your system and see if that is what is causing the performance difference.
In the long run, would performance of a single game make you change one or more pieces of hardware?