And that is the other consideration. You would need full platform upgrade, CPU, motherboard and RAM, to gain a minuscule improvement in IPC and four extra threads that won't be all that beneficial to you anyhow for a lot of games unless you're multitasking with other processes like recording or streaming as well. I don't really know of any games that definitively use more than 8 threads, well, even now. Maybe some, but not a lot. If you have a lot of background processes running it could certainly help in that area, but again, maybe not enough to warrant a full platform upgrade.
Now if you wanted to go Ryzen 7 or Intel i7, that would be different, at least to some degree, because you'd see an IPC improvement AND more threads, in both cases, but I'm still not certain that for 60FPS gaming at 1080p, those are either necessary or beneficial when I believe that what you have now is capable of doing that with either of those cards anyhow, unless you are also wanting to record and stream, or any other type of heavy multitasking situation.