Can run either on a decent 550w psu all day long. The 1060 will run on a 450w, but if looking at OC, a 550w would be a better option.
Ran my i7-3770K @ 4.9GHz and gtx970 @ 124%OC for 6 years on Evga G2 550w, and it's still running a year later. No worries. Gtx970/980 same thing basically.
You'd need a 980ti + OC to consider a 650w. I don't recommend anything at 500/600w, they aren't that good quality mostly.
Depends on the card. The 1060-6Gb/980 go head to head, some games the 1060 does 5fps± better, some games the 980 does 5fps± better, so overall the same thing. I'd take a 980 over a 1060-3Gb if prices are equitable, or the 1060-3Gb if there's a decent price difference, but given the choice, it's moot with a 980/1060-6Gb, whichever is cheaper, or if one is used and other new etc.