It really is pretty neck and neck. Personally I'd say 2060 just to keep it simple. Probably one of the best options if you're sticking to those resolutions and not feeding a high refresh rate display. You'll have a good time there. You get a new card, and potentially a nice one for the money, but that is to say you have the freedom of selection there. Don't get me wrong, the 1080 comes out on top most times, but it's not worth paying even a little mark-up or going used imo. There are 1080 blower cards going for the same money as some of the non-blower 2060's right now. Worth noting with the 2060... it's a cut down 2070. Lower TDP and a smaller die than big daddy RTX and son, so it runs pretty cool. Should even run a little cooler than a 1080, under the same cooler. A lot of the partner cards come equipped with great coolers as well. A few of the high-end ones come with monster heatsinks on them, sometimes for just a little more than base models and still less than or same cost compared to a *good* used 1080. Might be worth it just for that, if you're concerned with thermals or noise at all. Also ensures you'll generally get 1080 level performance at those resolutions. Many of them can be taken up to ~2ghz with minimal tweaking in afterburner... and still run a little cooler than a 1080 would.
And if you're at all interested in seeing RTX for yourself, that is a nice bonus with the 2060. RTX on is playable at 1080/60 with this GPU, though you may have to bring some settings down. It's not nearly as bad as its been made out to be. I can speak from personal experience playing Metro Exodus with RTX and quality settings on high. No crappy dlss. The difference is there and for the most part it holds 60fps no problem. Few small dips here and there, but otherwise I can only say positive things about it. Though that is a huge rabbit hole right now and it's probably best to just leave it there. Comparing it to a 1080, RT is just extra icing. Neither here nor there sort of thing.