Are you doing a new build or dropping a card into a current rig? Is this for 1080p or 1440p?
Here's how I like to think of it:
GTX 1060 6gb average 83 FPS in 1080p
RX 480 average 77 FPS in 1080p
GTX 970 average 69 FPS in 1080p (all numbers using PCGamer's sixteen game average, it isn't perfect but suitable for this analysis)
At $179 for the 970 you get .38 FPS/$
At $229 for a 1060 you get .36 FPS/$
At $209 for an RX 480 you get .37 FPS/$
Based upon those numbers the better value play is the GTX 970. However there are other factors, so bear with me. If playing in 1440p, the numbers are different (I won't do another analysis).
Also, if you are doing a new build you really are best factoring the performance/$ for the entire machine as...