Yes, the i5 will perform better. It also costs substantially more. I take it you are going to overclock since you want a k series? If so, better factor in the extra money for a Z87 series motherboard, and aftermarket cooler too. Same goes for the FX; decent motherboard (if you intend on going to town overclocking, a 990 chipset motherboard. Light overclocking; 970 with at least 4+2 power phases) and aftermarket cooler.
As for bottlenecking; No, the FX 6300 will not bottleneck the gpu. The i5 will perform better overall, but the FX will still do the job. More than do the job if you decide to overclock it.
If overclocking isn't your thing, then either save money and take the slight performance hit with the FX 6300/8320 at stock, go for bronze with an i5 4440, silver with the i5 4570 or gold with the 4670 (without the k). The 8 core FX chips come into their own with Battlefield 4. Something to add to your equation.
Whatever you choose, know that you will be having fun playing the game with any of the above, so try not to worry too much.