Your power supply should easily handle the GTX 660. RAM does not consume much power at all (maybe around ~7-10w max) so adding more RAM will not be significant in terms of power.
The problem is that not quite sure, because at past, i have had serious problems with power supplies.
With this Setup (Overclocked), My power supply (Corsair TX650W V2) was broken , at today my setup is not overclocked but i dont know what the diference in terms of power.
On the other hand the maximum power of my actual graphic card is 108W (as specified by 3DMark) and have a big difference (40W) with my possible new graphic card.
650W is enough, in fact you would probably have dual 660's in that system and still be fine. Problems in the past could have been caused by other things than the PSU or simply bad quality PSU's.
I looking for a Nvidia because im not very happy with my actual Sapphire HD 5770, it cost me 4 years ago 260 €, and never got the performance I expect.
Because of this, i looking for a nvidia chipset, but i don't know if there are a very big difference between GTX 660, GTX 670, GTX 650.
Anyway if there are a big difference with a particular chipset of ATI, I could buy it without problems.
The 7870 XT is a better performing card than the 660 and the reviews/benchmarks shows this quite clearly. Wanting Nvidia solely based on the experience you had with a GPU from 4 years ago seems a little off but your choice of course.
I don't know which expectation you have so I can't tell you which card is best for your needs, all I can tell you is the XT is better than the 660.