Perf/$ is pretty linear from a $240 480 to a $400 1070, placing the 1060 on that curve at $240-$300 and NV will easily win just by the virtue of perf/w, OC potential and massively better mindshare alone.
True. We already know NV's sales aren't correlated with perf/$ against AMD/ATI. (780 vs. 290 or 290X vs. 780Ti or 280X vs. 770 2-4GB, 260 vs. HD4870, HD6950 vs. GTX570, HD7970 1Ghz vs. GTX670, R9 290X vs. 980, etc.)
The mainstream PC gamer has to be very careful on this one. The extra $ spent on the 8GB RX 480 is better spent on a faster CPU instead. Move up from an i3 to an i5, from a stock i5 to an i5 K. It also doesn't matter if AMD claims that RX 480 was designed for 3-4 years in mind. It's a 2 year or less GPU. For that reason I question spending $40 more for the RX 480 8GB version. The issue with GTX1060 3GB is that for modern games that's too risky. Otoh, if GTX1060 6GB is $279.99, that's an $80 difference between that card and the $199 RX 480 4GB. We would then come full circle again and I'd recommend the mainstream/performance gamer spend the extra $80 towards a faster CPU that will last 5 years. No one had an issue recommending 3.5GB 970, 4GB 290/290X/980 for all of last year so there is no particular reason to even go for a 6-8GB card for this performance class over an 4GB card for 1080p gaming.
As you said though, the NV brand name will ensure they will be able to sell VRAM gimped 1060 3GB over RX 480 4GB. The hilarious part is that NV PR/marketing will not be able to use that 4GB is insufficient for 1080p gaming against a GTX1060 6GB but then still be able to recommend GTX1060 3GB over the RX 480 4GB. For that reason, AIB RX 480 4GB will likely be the best mainstream card in 2016 as long as AIBs can hit $210-220 prices.
Knowing NV though having a $239-249 GTX1060 6GB creates too large of a gap with the 1070, unless they later introduce the GTX1060Ti. I am thinking they will price it much closer to $279-299 than $239-249.
$199 RX 480 4GB
vs.
$299 GTX1060 6GB = 50% more expensive
$279 GTX1060 6GB = 40% more expensive
$249 GTX1060 6GB = 25% more expensive
In all of these cases, the GTX1060 6GB is a worse price/performance card.
In summary: The budget/performance gamer will be way better off either putting the extra savings towards a next generation 2018 GPU upgrade
if GTX1060 costs $279-299 ($80-100 is a LOT of $ towards a next gen 2018 $200-225 RX 480 successor that would make the upgrade just $120-145) OR putting it towards a faster CPU for longevity. Unless the GTX1060 6GB costs $249, RX 480 4GB will be the best value at
$199 among all of these cards. The extra 10-15% performance isn't going to matter over 2 years but moving from an i3 to an i5, or i5 to i5K is $ well spent. If GTX1060 6GB costs $279-299, then we'd looking at moving from an i5 6600K to an i7 6700/K for a new system build/platform upgrade. In that case, it's not even a contest in favour of the i7 6700K + RX 480 4GB >>>>>> i5 6600K + GTX 1060 6GB.