i5 8600K vs Ryzen 1600X?

Just gaming? Get the i5. It wins by a lot in single-core performance, and the upgrade to 6 cores instead of 4 from the previous generations will help smooth out the framerate when other stuff is open in the background. But if you're also going to record or livestream, then the extra threads on the Ryzen 5 will help more with that.

One thing to keep in mind is the motherboard. With a Ryzen 5 you can use a B350 motherboard, which you can find for around $70. For the i5 you'll need Z370 (not backwards compatible with 100 or 200 series chipsets and the other 300 series ones aren't coming for a few more months), which starts at around $125.

I'd say the "Userbenchmark" site has screwed up figures for AMD for whatever reason..

Passmark does not have the figures for the 8600k yet, but it has the 8400k. Comparing both on userbenchmark, the 8600 is shown as 16% faster than the 8400.

The passmark rating for the 8400K is 10996. Add 16% = 12755

The Ryzen 1600X scores 14644 and as you say, the AM4 platform should be supported for a good few years.

The i5 8600K is $260, whereas the R5 1600X is $220, so I don't know why you think the i5 is cheaper. But anyways, the R5 1600X isn't the best value among the R5's, the R5 1600 is, it's $195, and it overclocks just as well as the 1600X does.

Also the Ryzen motherboards are much cheaper than the Intel ones right now.