Go with the 1060. It is newer tech and the power consumption and heat generated will be lower, as well as the performance will be equal to or better than the 780.
I don't know anything about either of these cards. But judging from the model numbers the 1060 is a higher resolution than the 780. I would assume that the 1060 will display at 1060 pixels whilst the 780 will display at 780 pixels/whatever. These are standard resolution specifications so I would keep the 1080. having said that asking a question like that on here will get you ten thousand opinions all different LOL. Good luck.
Ah, I really recommend selling the 780 and cancel the 1060 3GB purchase (if you can) if you're a serious gamer (that's different than heavy gamer).
I'm playing Gears of War 4 and the VRAM is passing 3GB by far (total use with the desktop reaches 4GB) causing occasional stutter with new textures showing up so I had to reduce two texture settings from ultra to high to get ~2.4GB game usage to reduce the stutter (still exceeded 3GB a little sometimes with the desktop usage). The memory bus width on my GTX 680 4GB is 256-bit, higher than that on the 1060 3GB which means even slower texture swapping let alone the less size that causes using the much slower system RAM (which reached a crazy 14GB total of texture buffering at some point because of that!).
The 780 has faster memory bus width but is it at least 4GB? Games started to use more VRAM lately even at 1080p like with Gears of War 4.
Later models are better in terms of power and support, of course, but performance is always the target for gamers specially if it is noticeable. Try finding some gameplay of the same game on both cards on Youtube to compare. This could help.
And no, the model number indicates direct rule to do with the resolution. A lower model number could be able to use higher resolution that a higher model number.