Looking at it logistically, ATi's part will probably consume more power.
Rv670 is 105W on 55nm.
R680 is 190W, and is Rv670x2, 55nm.
Now, while "R700" (or whatever the single die is named) may be on 45nm, it seems likely (at this point in time) that it will be on 55nm, be it that samples are supposedly out and such. I take this to mean we can't expect much power savings per spec using the same architecture.
I would assume each R700 chip will be an increase of the spec of RV670, with a little pixie dust thrown in such as changing of how AA is done (ROPs as well as shaders, or whatever). Let's say 50% increase in spec, which is realistic. While not an exact science, it would put it at around 150W for the single core part, and (if R680 is any indication) a dual core part around 280ish. Granted R680 has higher clocks than a single 3870 and thus power savings may be more than what we see now if the R700x2 has similar clocks to the single core part.
While whatever the dual core part of R700 is may not be similar to R680, there is only so much wiggle room of how much juice two chips will need.
I believe the single core part will aim for <150W, or one power connector on a pci-e v1 board (75W from slot, 75 from 6-pin), none on a pci-e 2.0 board, as it can provide 150w of juice. This just seems logical to me on a mainstream scale, and doable with a 50% increase in spec, while it might be tight. 140-150W?
I also believe the X2 part will shoot for < 300W, and will achieve wiggle room for higher clocks from combining the two chips on one pcb, like we see in the 3870x2. The 300W number is derived from the pci-e 2.0 spec, as well as the logical amount of connectors (2 six pins on a pci-e 2.0 board or 1 six pin and 1 eight pin on a pci-e v1 board). At best I imagine we see similar results to R680, and about a 20% efficiency (250W) and at worst similar to what we see on R680 through pure wattage differance (20W or so...260-280W?). It's impossible to guess considering the X2 product of the R7xx generation will be completely different than R680, and we don't know how the 2 chips, 1 board scales through the use of bigger chips. I think nearing the cusp of 150w for a single part, and 250-280W for a dually is a reasonable guess though.
Personally, I don't think we can ask for much more (less) than that unless the actual chip technology incorporates a more efficient way to do the same tasks or the architecture is dramatically different than R600.