As others have said, it's best you instead go for a Ryzen 1600 or Ryzen 1700, especially since you're gaming at 4K. Mostly you'll only get a little above 60 FPS at 4K with a mainstream GPU, maybe a 120 at most. For this purpose, a Ryzen CPU will trump over the 7700K and the 7600K both due to its competitive price as well as future-proofing. A Ryzen 1600 has 6 cores and 12 threads, costs less than a 7600K, comes with a good stock cooler, and is overclockable even with cheaper B350 motherboards.
The higher clock speeds of the Intel CPUs will only benefit at high refresh rates, i.e., at 144 FPS or greater. At 4K, you'll rarely be getting such FPS, plus all 4K monitors are only 60 Hz, so your monitor can't show more than 60 FPS anyway. So it's best you go for a Ryzen CPU, pair it with a B350 or X370(depending on budget) motherboard, and use the stock cooler(if it is a non-X chip). You can overclock as well if you want to, but then it's best you get an aftermarket cooler for better results.
Either way, for 4K gaming, a Ryzen will win over both the Intel CPUs you have mentioned, not just in performance but in value as well as future-proofing. '
If you still insist on the Intel CPUs, get the 7700K, because the hyperthreading might help the CPU last a tad bit longer in games.