I definitely would get the GTX1060 6GB
(AMD RX-480 8GB is also worth considering. If you have a good CPU that's also a good choice. It's not quite as good for older titles but pulling ahead for newer so one isn't definitely better than the other.)
1) POWER PHASES aren't directly related to overclocking.
The GTX1060 and newer GPU's are running close to their maximum already which is why there's little overclocking left.
2) 3GB is not enough for some games currently to prevent stutter, and that's only going to get worse as many newer games are VRAM hungry. Proven with the GTX1060 3GB card vs underclocked GTX1060 6GB.
3) Performance:
https://www.techpowerup.com/reviews/NVIDIA/GeForce_GTX_1060/26.html
The GTX780Ti if it overclocks well will close the gap, but again I don't recommend it due to VRAM.
Also, the newer cards are much quieter and even can disable the fans. In addition, is that USED? If so, if it fails you are SOL.
4) No mention of CPU as well. If it's relatively weak it will bottleneck (but it varies by the game).
5) *You can expect about 2x the FPS in games with GTX1060 6GB vs your GTX770.
6) You can still TWEAK a GTX1060 but it's more complicated. On my GTX1080 I did THIS:
a) 5% overclock on my FTW card, then
b) used EVGA Precision and clicked "MANUAL" for the frequency/voltage graph. This takes several minutes but will optimize the voltage for each of the frequency points to minimize the heat and thus reduce throttling due to temperature.
So I gained 10% or so in some games but it varies as to whether the game is even running at the throttle point.