I think it's better to compare stock vs. stock because you can overclock the 1060 as well. If you want, you can compare the OC potential of cards as well since that can vary depending on architecture or just the limitations of a card if it only has a 6-pin.
Well if we are to restrict ourselves to stock configurations then as I said before the 1060 3GB is matched by a 970. However, Maxwell was very good at overclocking and some AIB card models of the 970 would probably be ~10-15% faster than stock performance taking it closer to the 6GB variant of the 1060.
On AMD's side Polaris brought a slight price reduction in this segment before the crypto boom, but it wasn't a convincing enough upgrade for all the R9 290/290x/390/390x users.
Which is why I am saying that the 200-300$ segment hasn't seen a significant uplift in performance since the GTX 970 dropped in price to under 300$ - which was what, 3 years ago?
If we are lucky and this upcoming card is priced between 200-300$, then finally we'll see a decent jump in this segment if the rumored performance is around that of the GTX 1070.