The 1060 3GB version is a definite 'no' for me. I've mentioned this in a couple of other threads but look at Doom Vulkan benchmarks on the 460 vs. the 380. The 380 is a significantly more powerful card (midrange vs. 460's bargain range) and beats it thoroughly in all cases except this one. Why does it lose in this instance? Because it runs out of RAM having 2GB vs. the 460's 4GB. Right now, Doom on Vulkan is the exception but I think over the next eighteen months, 4GB will become the baseline for mid-range performance. I'm actually fairly confident on that. Buying a new 3GB card at this point in time is a bad mistake.
With the 3GB 1060 taken out of consideration however, I think both are good and competitive with each other. The 1060 is a bit more powerful however, it also still costs more. It also (I think?) has SLi disabled meaning there's no easy upgrade path from it whereas the 480 still has that. I think mGPU is going to be a more common and better supported practice from here forward. (Caveat: some respectable forum posters disagree with me on that).
But most significantly, the 480 will give you Freesync support. That's a major plus over the 1060's Gsync support as I'm optomistic Gsync will lose out in the format wars. So I personally would recommend the 480 over the 1060. I think it has better prospects and is not much weaker.