This whole thing is worth it/not worth it from a perspective standpoint, basically.
If you're looking at sheer numbers, probably not.
If you're looking at if you'll be satisfied with an upgrade and want an upgrade because it'll help with productivity, better gaming and better speed...probably so.
Initially, I recently built a system that had an R5 1600 and thoroughly enjoyed its performance over the FX 8350 it replaced. I later built my dad a system to supercede his aged-out A4-centered system (the dust that resided in the case makes me wonder how a dust bunny colony didn't attack me on sight when I opened the case up to scavenge his 500GB HDD out of it to put into the new system as a secondary storage option) and dropped my 1600 into it. In turn, I used that to justify upgrading myself to a 2700X and dropped it into my current build...I probably didn't
need it, but POWER, BABY!!!! I'm also dabbling with streaming, and the extra two cores help a lot with that. Otherwise, I would have just stayed with my 1600, as it's still a lovely gaming CPU.
If you do decide to upgrade, I'd go with the 3600 over the 3600X; everything I've seen says you're paying the extra $50 for the Wraith Spire cooler over the Stealth with barely noticeable variances in Hz/IPC. I'm assuming, since you have a 1600X, you have your own aftermarket cooler since it didn't come with one...continue to use that one and perhaps sell the Stealth.
Also, make sure to upgrade the BIOS to whatever the newest one is that will support the 3000 series with the most modern tweaks to it that keep the voltage draw a little less crazy. Depending on what motherboard you have, it may or may not have been posted to your manufacturer's support page...I believe it's AGESA 1.0.0.4...the 570 chipset motherboards will likely have it available while the older chipsets are coming slower.
For my personal use case, I found the 2700X a useful upgrade...it even makes Windows boot and shut down faster, and the Wraith Prism is both extremely pretty and a much beefier cooler where temps are noticeably better...but that's just me. Do what makes YOU happy, and if that includes dropping ~$190 for a 3600 upgrade for better speeds that you'll notice while getting personal satisfaction that you've gotten said upgrade, go for it. If you want to wait for the 4000s, however, then wait. You know your desires and use case. Apply them into the equation and decide accordingly.