This is a difficult to answer question. Power consumption depends on mostly hardware. One might think DOS being so bare use less power ? Try to do an experiement on a notebook and boot a linux that is not bootable(because of whatever error and halt at init). The fan would turn on very soon even you are not running anything. This is related to power saving feature of modern day hardware. Without the proper OS, they would be there doing nothing but still consume quite some energy.

So I won't be surprise to see two identical machine one running DOS, another XP and that the XP one use less power, as DOS may not have the facility to turn off the HD, or the screen and for some mobile GPU.

On a desktop which don't have any power saving device, the difference may be minimal with DOS may be using less but should be almost the same on idle.

So I would say this question itself is a bit off.