Why stay away from the 1060? If you are saying that because of DX12, do you not think that NVidia will get to grips with it?
I can't say that with 100% certainty, but my sense is yes, so that's my opinion.
Here's the thing (and I honestly am trying to get this straight as I've put money down for a Nitro+):
There's DX12 as an API. This is all the multi-core/multi-engine/multi-GPU etc stuff and the new paradigm.
Then, there's DX12 features (the stuff that MS packages into feature levels and even moves around back and forth).
In the former (the API, not the features), AMD will always get a 5-10% advantage as demonstrated several times already (and yes, it's only up to 10%, the rest of the gains have nothing to do with the ability to run async in parallel instead of using preemption). It's not huge (like some people make it out to be), but it's significant (especially for otherwise closely matched cards such as the 1060 and 480) and it's something all DX12 games will have.
The second thing that leads me to picking the 480 is its extra power: the 1060 is fewer teraflops worth of power, which doesn't show in DX11/OpenGL. But the DX12/Vulkan titles can and will tap into it. The AMD drivers will no longer stand in their way.
In a price-sensitive segment, one's got to think about resale value down the line and stuff like that. Two years from now, my bet (and that's why I put my money for a 480) is that I will be able to sell it for more in order to upgrade. Plus I pay a little less now. Sure I've got to tolerate 10% fewer FPS in DX11 titles (not even that much with my non-reference card), but I can live with that for a year.
Where it gets complicated is with features.
For example, DX12_1 feature set contains Conservative Rasterization and Rasterizer Ordered Views. This stuff is currently only in NVidia cards as AMD don't implement them (and have not found anything hinting whether and when they intend to). Once games start utilising these (I think RotTR does) they will give some advantage to NVidia. How much remains to be seen, but you can't rule out the possibility for something as significant as async and the 10% AMD gets from that. It also remains to be seen whether AMD will at some point support them.
A similar thing exists with DX12_0 where NVidia is lacking in support but AMD is already providing that stuff so that's actually another plus for AMD.
In any case, all indication is that the more DX12/Vulkan games arrive, the less attractive the 1060 will look over the 480. That's my main bet.