Especially for gaming, you would want the 3600. It has MUCH stronger single core performance and even today there are a lot more games that can use a strong single core to full advantage than there are games that are optimized well for highly threaded performance. Some, but not all, or even most, at least not beyond a few. So having both strong cores and many of them, is definitely a good thing.
2nd Gen Ryzen like the 2600 has single core performance that is only about on par with the 3rd Gen Intel 3770k, while the 3600 has single core performance that is almost identical to that of the Intel 9th Gen 9700k. So yes, there is a HUGE difference in gaming performance between the 2600 and 3600, well beyond the 65 dollar difference.
People with Ryzen 5 2600 CPUs are and have been upgrading to 3rd Gen Ryzen processors like the 3600, 3600x and 3700x for a reason. That reason is that the performance is an exceptional leap between generations like we've seldom seen before aside from one or two occasions historically.
If you are only looking for 60fps at 1080p, and nothing more, then the 2600 will MOSTLY do what you want it to do, but if you are looking for anything beyond that, or do not want to encounter ANY games where you are not able to achieve that, then it would be 65 bucks worth spending.