I was in the same position, you mainly have to weigh up the pros, cons and what you want from your purchase.
For me it was mainly bang for your buck, and after 15 years of Intel, I went for AMD ryzen.
With ryzen the AM4 motherboards are generally cheaper than the Intel supported ones, however as it is new technology there are still some gremlins but they're being ironed out with each bios revision, I had been sent an early mobo which didn't have the bios version that supported ryzen 5 and had to send it back to get updated (would only work with ryzen 7) bit of a ballache but it's absolutely fine now. Also ryzen loves fast RAM, the sweet spot as people are saying is the 3200mhz modules, I went for 3000mhz as that's what my budget could afford, again this is where the mobo bios rears it's ugly head and you'll have to tinker to get those speeds (for me it was simple enabling XMP in the bios to get it up to advertised speeds, again something that should get sorted with newer bios) this is just my experience with my particular model of motherboard, others could be just fine (gigabyte ga ab350 gaming 3)
Where the ryzen stands out is in the multithreaded performance, it far exceeds the Intel equivalent, but the single and quad core is slightly behind. I went for the ryzen 5 1600 and Oc'ed it to 3.8 (I got an after market cooler, despite the stock cooler being very adequate) so the Intel equivalent would be the 7600k.
I am very happy with my purchase and performance, it was a worthy upgrade on my i5 2500 and games perform just fine.
It all comes down to cost and whether you will utilise that multithreaded advantage, if you're purely in it for gaming then both are just fine but you will see better performance in the Intel equivalents, but the ryzen is by no means a slouch.
It's also worth noting that ryzen chips do not come with inbuilt graphics processors, unlike Intel. Also check if your model comes with a cooler, for instance the 1600 comes with the stock cooler for £200, for £230 you can get the 1600x (slightly faster stock clock speeds) but it does not come with a cooler, so you have to factor in that extra cost
