I own both a ryzen 1500x and a 5820k. 1500x in the servercomputer and the 5820k for my main desktop. I would absolutely say that the 5820k is a waay better overclocker than the 1500x that i have. And i guess the 1600x is built on the same die. I am running my 5820k at 4.8 ghz and scoring 1456 on cinebench r15 with a single core score of just over 180. So for both gaming, media and desktop purposes the 5820k is the superior choice. It is slightly more expensive however, But it is a really fast processor that in my experience is very easy to overclock. My father recently bought a 6800k. Which is basically the "newer" 5820k. But it is way worse, in all possible ways. Can barely reach 4.4 stable. Should also add that i use a 480mm radiator with custom water cooling to cool my 5820k. But a 240 AIO or similiar would probably produce enough cooling to satisfy it's needs. Ran it at 4.6 with the noctua dh15 for about a year.
I have played around a bit with the 1500x and i must say that, as a slight fanboy of intel, that it is damn impressive. Passed 3.8ghz on stock cooling reaching a max of 60c. I will go to the store tomorrow to buy 240 AIO cooler to see how high i can reach, at 145 single core score and 850 multicore score now it is actually pretty amazing. It is already now up and battling with 2-3 generations older i7's. Which is quite impressive considering the i7's have always been a long term choice. Will be trying to ramp it up to 4.0 or 4.2 after i bought a new cooler. As of now i can almost recommend buying a ryzen 5 or 7 for gaming. They seem to be able to get the job done if you buy a decent aftermarket cooler and play around with them a little. But the true gaming cpu is still the 7700k. Both regarding it's price and it's single core performance. Perhaps we will see even better results when the new i7's and i9's roll out later this year. I am slightly dissappointed overall with the ryzen overclocking experience though. But that is mostly because i love to fiddle with voltages, timings and such.