Neither should really draw more power than the other, barring any serious overclocks one has over the other. Your links are broken, by the way. But if you're that concerned about power draw, go for a 7770 instead: it's close to the 6850 in performance, can overclock past it, and draws less power.
Remember that both these cards are at the stock clocks though, and also that they are both reference models, and should both run much cooler. My 7770 will usually top out at about 53C when I'm playing games with the fan topping out at around 55% only.