If the 1060's were equal, with the only difference being the amount of VRAM, I could potentially see the argument for "overkill".
But that's not the case. The 3GB 1060 is a 'crippled' 1060 - realistically, it should've been called something else entirely.
It's likely going to end up somewhere between a 1050 (based on rumored spec) and a 1060. Something like a 1050 TI Boost or similar would likely have been a smarter/clearer naming convention for the card.
Either way, even the 3GB variant is a huge performance boost over a 960 which, as I mentioned to begin with, was a pretty poor investment (read "bang for buck") even when new....... kinda comparable to a 3GB 1060 today! (Not in a sense of raw performance, but in the poor "bang for buck" angle.
When I said at no greater than 1080p, that's pretty much the realistic expectation of the card.
A GTX 1060 6GB variant should be able to near max out most titles at 1080p.
The 3GB variant is close behind, but not quite as good a performer (probably 'high' on most titles)
If you go beyond 1080p, the GTX 1070 is the card for 1440p and is a respectable performer at 4K.
A GTX 1080 or Titan X(p) would be the 'ideal' at 4K.