The 8600K will usually win-out in most titles, more often than not - Overclocked, 1600 can catch up some, but equally the 8600K can OC to reopen the gap. The differences lie moreso in the 'minimum' FPS.
https://www.techpowerup.com/reviews/Intel/Core_i5_8600K/14.html
Of course, it'll depend on the GPU you want to pair it with - and the resolution you want to play at.
At 4K, for example, you'll be hard pressed to find much of a performance difference between either chip.
Yes, the AM4 socket is to be supported through 2020 but, as you stated you don't plan on swapping CPUs in 2-3 years, the chances of that being a worthwhile consideration are slim.
sizzling :
Also I'm not convinced AMD's next gen CPU's will work with 300 series based on an article I read. Yes AMD said they were sticking with AM4 but that does not automatically mean 300 series board will definitely support next gen CPU's. Look at Intel 1151 socket, Coffee Lake uses the same socket but cannot use 100 or 200 series boards.
Logically, AMD are still making up ground on Intel so, while they theoretically could 'pull and Intel' and require new chipsets, I highly doubt it. They've made the point numerous times than the AM4 socket will be supported through 2020. Now, that doesn't expressly mean "chipsets still compatible through 2020", but it would be a very stupid move on AMD's part to not 'truly' support it through 2020. They don't currently have the luxury to screw over their customers :lol:
Ryzen is a great gaming chip, from a "value" standpoint and is usually my recommendation but, given you're only looking at $50 or so, the 8600K would be my personal preference..... although you can't really go wrong with either, the gap is small enough that the 8600K makes sense (to me), assuming 1080p or 1440p gaming..
Today, you also have to consider the differences in RAM prices (that are all ridiculously high anyway).
Ryzen really benefits from 3000MHz or greater..... Intel platforms, not so much. You can net very similar performance with anything from 2400MHz to 3000MHz+
You're paying a minimum of $15-$20 premium for 3000MHz or greater, 2x8GB. Not a huge difference, but it's still a difference.
$255 + $180 (3000MHz) = $435 (Ryzen)
$310 + $160 (2400MHz) = $470 (Intel)
Gap gets even closer when you factor the 'complete' cost to the builds.
While it's difficult not to get caught worrying about cores/threads.... from a strict gaming standpoint, I think we're still a few years away from >6 cores being commonplace in gaming. If your workloads were more than just gaming, and the cores/threads made sense in those workloads, the 1600 would be a great buy.