This is not an easy one to answer as you will have fans for both CPU's giving you different answers. The Ryzen 1600 CPU's are great as they give you 6 cores and 12 threads, thats 6 more threads than the 8600 but the 8600 has a higher boost frequency. On the other hand if you are only and I repeat only looking to Gaming with some light workloads then the 8600 especially the K version will do a fantastic job accross all games and especailly if you have a high refresh rate monitor. Most 8600K's will also overclock extremly well to at least 4.8 but to 5GHz as well.
On the 1600 side you will still get good frame rates in gaming, just not as good as the 8600, but you will get a whole heap of power for more work related procesess like...