I said not much, not nothing. Comparing against even the Fury version of Fiji it's a fairly modest improvement - yeah it's a big improvement over Hawaii but bear in mind a lot of that is from architectural improvements already seen in Fiji (like I say I very much doubt they've regressed in architectural efficiency since Fiji).
https://www.techpowerup.com/reviews/AMD/RX_480/25.html
They don't include the Nano in those charts but looking at the
Nano review it's not hugely different, but as you say that's basically best case on 28nm vs worst-case on 14nm so not a life-for-like comparison.
On the other hand Nvidia seem to have gained a large improvement moving to 16nm despite a significant increase in clock speed.
I agree though it will be interesting to see how Polaris/Vega do with future lower-voltage parts.