The only difference between the two is the 9600k has slightly higher stock clock speeds and might be slightly better at overclocking with better thermals. Otherwise they are the same CPU with the same architecture and IPC.
The performance difference between the two in games will be little to nothing. At the same clock speed they should perform exactly the same.
It will be marginally better because it has higher base clocks. It should have lower temps due to solder, which will give it a little bit more headroom for overclocking. If you are big into overclocking, then it has an appeal over the 8600k. But if not, then I would go with whichever is cheaper.