TPU lists a peak gaming power measurement of 118W for GTX 960, compared to 184W for GTX 980. The GTX 1080 matches the 980 exactly in power usage.
Does this mean we should expect the same figure (roughly 120W) for GTX 1060? Maybe. The GTX 960 ran at the same clock rate as the 980, and leaks indicate that the 1060 will likewise share the same clock rate used by the 1080. But there's one important difference: while GM206 was half of a GM204 in pretty much every respect, GP106 has a memory bus 75% as wide as that of the GP104, and with a clock rate just as high as the GTX 1070. The memory controller is often one of the more power-hungry aspects of a video card. This means GTX 1060 might go in closer to 130W peak gaming than 120W. I suppose we'll find out soon enough.
GTX 1060 FE will definitely beat reference RX 480 in perf/watt, based on what we've seen so far. Depending on how AMD fixes the power management issues, it might be closer than most people are assuming; undervolting could get RX 480 down from ~160W to 130-140W. (Pushing too much voltage has been AMD's Achilles heel for a long time.) Most people will eventually be buying AIB cards instead of reference for both RX 480 and GTX 1060, so it'll be interesting to see how this competition shakes out in both raw performance and perf/watt.
A hypothetical P10 card with GDDR5X, better binning, and more precise voltage settings could match GTX 1060's perf/watt or perhaps even beat it. Higher memory clocks mean higher power consumption (this is one reason HBM is so efficient: it uses a very wide and slow memory bus). Switching from 8GB/s GDDR5 to 10GB/s GDDR5X would let AMD drop the memory clock from 2000 MHz to 1250 MHz while simultaneously increasing bandwidth by 25%. That could make a substantial difference.
So far, if you look at all the reviews, Pascal very much more strictly adhere to the TDP limit than Maxwell AND gives more room for allowrance. Both 1070 and 1080 operate below their TDP of 150 and 180W respectively when it comes to peak gaming.
Then, there's the fact that the FE cards can overclock just as well as the aftermarket cards. What's damning is that the GTX 970 was rated at 145W yet most AIB reference cards were rated at 170W. For the GTX 1070, this is no longer the case. Rated at 150W, and AIB reference clocked cards are also rated at 150W.
Surely, the perf/watt for a GTX 1060 will be lower than the big boys, and historically the x60 perf/watt has always been lower. But even then, it would be 150% of the perf/watt of a RX 480. There is no way a RX 480 will match the GTX 1060 in this regards.
AMD has also said that the RX 470 will have the better perf/watt. This is the opposite of Nvidia, where the GTX 1080 has better perf/watt than 1070. The conclusion that can be made is AMD squeezed every last bit out of the RX 480 thus destabalizing the optimal perf/watt.
It's all moot, but if the GTX 1060 has lower than 140% of perf/watt than RX 480 it would be a disappointment sufficient to say.