Unfortunately, the performance gain in the middle of that gap is pretty non-linear. The better video card is wasted without the Intel processor, and the Intel processor is idles without a beefy graphics card to back it up.
Specifying the games you are interested in would help with a recommendation.
It's an extreme example, an outlier really, but in Guild Wars 2, 290X crossfire will only deliver "teen" fps in areas on an FX chip, while a 265 paired with an i5 will comfortably max the game and deliver framerates in the 30's in the same areas - still CPU limited, as the 265 would comfortably deliver 60+ FPS with an infinitely fast CPU. There are no settings you can disable to reduce the CPU needs of that game. CPU limitations don't change with the video cards paired with them.
EDIT:
A faster video card allows you to crank up more settings in more games, but you want to balance that with spending on a CPU so that you're CPU limited at playable framerates in as few games as possible. I'm fine with dropping shadows a notch in most games to maintain high FPS so I don't mind spending proportionally more on a CPU that will allow higher framerates.
In most games an FX-6300 will perform very well, so where this balance lies depends on what OP is doing.