Don't have the time to do a ton of data collection, but since it came up in another thread. I have a Zotac Zbox CI 327 running a celeron 3450 which is a bit older, but basically a decent base for an x86 router (it has dual ethernet built in for example, it's fanless, it was pretty cheap). I'm running it as a media pc. At idle my kill-a-watt meter shows between 4 and 5 watts (it kind of oscillates back and forth). Running a speed test it shows 7-9 watts, with a few peaks to about 11 watts. This is actually running firefox browser on the box and doing a waveform bufferbloat test on the box.
Power consumption is the box + its power supply + several USB hubs and various USB devices, but doesn't include the monitor. Also it's power factor corrected, not a VA measurement.
If I were going to guess at its power draw in real life as a headless router, I'd guess less than 5.5 watts long term avg on this basis, and very likely something like 4.5 to 5.