I put the 1060 into a much older PC (link to follow) and it benchmarked fairly close to newer PCs.
The real problem I see is that the 970 to 1060 may be a small gain overall.
Here's me putting the 1060 into an old Core2Quad PC:
I am thinking on upgrading my PC with an NVIDIA GTX 1060 6GB videocard(current one is GTX970 4GB) I will check out the space and the voltage if I have it, but my question would be:
With an Intel Core i7 6700 3.4 GHZ processor and 16Gb ram, will one of these be a bottleneck for videogaming, or does it worth to upgrade this system with the videocard, instead of buying a new PC?