Might want to look at GTX1660 and the upcoming (July 7) AMD Navi GPUs, since the GTX1060 and RX580 are >2.5 years old at this point.
I posted an AMD Polaris Undervolting Guide here.
I was able to pull about 30W out of my Factory-1305MHz RX480 without sacrificing any clockspeed. That pretty much brings it within striking distance of an untouched GTX1060 in power draw. Most results I've seen on RX570/RX580s are about the same.
Nvidia GPUs are a bit different since GPU Boost3.0 typically overclocks past the advertised boost clock speed anyway. I haven't looked too hard, but you'd need to find someone who's keeping an eye on that ACTUAL boost clock while undervolting. It all depends on how sophisticated GPU Boost3.0 actually is (aka, how conservative it's being when it adds voltage to get higher clocks while staying under the thermal limit). The GTX1060 starts at a lower power draw than an RX580, so like I said above, a zero gain for a GTX1060 tweak is a break even on power draw.
I don't have much experience with Afterburner or other 3rd party apps for tweaking Nvidia GPUs, but I do like AMD's built-in WattMan utility that runs within the driver already. I know the default Afterburner is simply a voltage/frequency offset [from max speed assumedly], whereas WattMan directly exposes all 7 of the performance states' Frequency and Voltage for an easy to understand result.
Main: i5-3570K, ASRock Z77 Pro4-M, MSI RX480 8G, 500GB Crucial BX100, 2 TB Samsung EcoGreen F4, 16GB 1600MHz G.Skill @1.25V, EVGA 550-G2, Silverstone PS07B
HTPC: A8-5600K, MSI FM2-A75IA-E53, 4TB Seagate SSHD, 8GB 1866MHz G.Skill, Crosley D-25 Case Mod