I've had Phenom II x6 1090t @ 4.0 GHz max Crysis3 using Tom's recommended 2x SMAA with an R9 280 (HD7950 GHz ed) Crossfire setup. All 6 CPU cores were loaded at 90-95%, Both GPUs were loaded to 95-99%. FPS was between 40-60 with an average around 50.
So...many modern games WILL use more than 4 cores, and a 6 core is very capable.
I've also had/built/tested gaming rigs with Multiple 1090t, FX 6300, FX 6350, FX 8350 and FX 9590 CPUs. The performance gain going from 6 to 8 cores is moderate. The voltage, amperage and power use goes up quite a bit though. You need rock solid motherboard and cooling to support it. A 6 core is much easier to work with.
I would suggest good cooling and an OC on the 6 core instead. 4.5-4.6GHz on an FX 6300 will run nicely, (* similar to an i5 4460 or 4590). You don't need as much power, it will generate less heat, it will stress the motherboard less, but it sill still support a high end GPU with good performance.
Here's a good example of an FX 6350 @ 4.8 with a GTX 970. FX 6300 @ 4.6 won't be far behind.
[video="https://www.youtube.com/watch?v=4ZHlo0DAI38"][/video]
And here's 2 examples of a recent build with that same CPU @ 4.6GHz on a single R9 280. This is performance WHILE CAPTURING VIDEO. When just gaming it's even better.
[video="https://www.youtube.com/watch?v=5M0AAdaArIo"][/video]
[video="https://www.youtube.com/watch?v=MpwMV32Fkfo"][/video]