Hi so this thread and it's replies have sparked some curiosity within me and encouraged me to do some testing.
I decided to test the power consumption and performance of my computer and will be sharing the results.
My system:
GPU: Sapphire RX 580 Nitro+ 8GB @1411Mhz
CPU: Ryzen 5 1600 @3.8Ghz 1.34375v
RAM: Corsair Vengeance 2x8GB DDR4-3200 CL16
MB: ASUS PRIME X370-Pro
PSU: Super Flower Leadex II 650W 80+ Gold
I did several benchmarks using Superposition and Heaven 4.0. All benchmarks were done in the extreme presets in 1080p. I measured the power consumption of the video card using MSI Afterburner and the total system power from an adapter plugged into the wall and the PC into the adapter.
Superposition
My RX580 peaked at 176 watts and my Total system power draw was jumping between 280W and 295W throughout the benchmark.
Not sure why it says the gpu is an RX470/480 8GB. It is definitely an RX580
Heaven 4.0
Not sure why but when running Heaven the GPU and system were running 10W lower than when in superposition even though in both benchmarks the card ran at 100% utilization. Also not sure why it says it's an RX 580 4GB when it is definetly an 8GB card.
Also from a Hardware Unboxed video they review a GTX 1070 Gaming X from MSI and from their power usage results it seems the stock power consumption should be near 254W for the total system power draw.
Here is the Hardware Unboxed video:
https://www.youtube.com/watch?v=3y2J1NJzioU
Regardless of which of these cards you buy I am more than positive your power supply can power your system comfortably until your next upgrade.
Now regarding which one you should get is totally up to your budget. The GTX 1070 is round about 40% faster than the RX 580 according to results on userbenchmark.com
If you find a GTX1070 that is below a 40% price difference between the RX580 you want rather get the GTX1070.
The RX 580 seems to fit better in your current build in my opinion, but both cards are more than adequate for your system if you play in 1080p.
The GTX1060 is great option as well, if is the 6GB variant and cheaper than the RX580.
Hope this helps!