ikaz :
Another option is RX 470 4GB you can get one for around $170-180 if you can't afford the 6GB 1060 it better than the 3GB version faster and more memory.
https://www.amazon.com/MSI-Radeon-RX-470-ARMOR/dp/B01N3TCNNW/ref=sr_1_1?s=pc&ie=UTF8&qid=1482536331&sr=1-1&keywords=rx+470+4gb
The RX 470 is not faster than the 3GB 1060. The only thing the 470 has going for it is that it's a little cheaper and has more VRAM. It does not perform better though.
The RX 480 4GB is an option if you want to go with an AMD card. I would not get a 470 when the 1060 3GB and RX 480 4GB are not much more expensive with better performance.
You asked about the 3GB 1060 vs the 6GB 1060 and in that comparison I would choose the 6GB 1060 for the reason I mentioned in my first post. When comparing the 470 and the 3GB 1060 I would not hesitate to choose the 3GB 1060 though. It's about 20% more powerful.