CharlesGrey: In theory the GTX 1060 and many older Nvidia GPUs do support Vulkan & DX12
Of course they do support it. It'd be kinda weird not to support a standard. They just don't gain a lot from DX12. But that's not exactly a "weakness" of Nvidia. It's more the case that AMD got rid of some problems they had with DX11.
AMD had two major problems with DX11 compared to Nvidia (since AMD switched to their GCN architecture):
1. CPU overhead. DX12 and Vulkan reduce CPU overhead
a lot! So AMD basically gets a "free boost" here.
2. They somehow never managed to make full use of all of their compute units on their GPUs. I have no idea why this is and why they never managed to solve this, but... yeah, this somehow is a problem for AMD. That's why the Fury X has some impressive numbers (the Fury X sounds absolutely sick on the data sheet) but doesn't perform anywhere near a less impressive sounding GTX 980 Ti or Titan X.
DX12 and Vulkan introduced a new way to handle different tasks concurrently (mainly "graphics" and "compute"). And this helps AMD to make better use of their compute units. In DX12 games, the Fury X beats the 980 Ti and Titan X (in most games DX12 is still slower than DX11, but that's another topic)! It finally makes use of the "impressive numbers".
CharlesGrey: just not as efficiently as the RX 480, correct?
That's the question... Nvidia never had the problem of massive CPU overhead and Nvidia never had a huge problem to make full use of their streaming multiprocessors (<- that's how Nvidia calls their compute units). They look bad in DX12 because they never had the problems that AMD just solved. They look bad because they always were good :/
Nvidia goes a different route for multi-engine stuff. AMD has its Asynchronous Compute Engine (a hardware based solution with a dedicated cache) and Nvidia has software controlled "dynamic load balancing". I can't say which of these two is more efficient. AMD's solution sounds better to me, but that's a way too technical topic.
What happens now, is that AMD's "old problem" meets the first DX12/Vulkan games. AMD has to throw out a powerful RX 480 at a low price to compete with a mid range card like the GTX 1060 (DX11). But when a game makes good use of DX12/Vulkan, the 480 suddenly competes with the GTX 1070.