Well, Apple is running a modified OS X on its iDevices, and Android is Linux based. Now, before you state the obvious: in both cases, the primary userland, that is, the userland that you're interacting with right now, is a stripped down power-optimized version.
And that's true of Windows 8.1 if you use the Metro UI too. Yes, OK, the desktop stuff is there, it's on "disk", ready to be swapped into memory if you want to run it, but it's not actually active in any serious way, it's waiting for a mouse click that isn't coming. Start your task manager now if you don't believe me, and take a look at the CPU usage of, say, Explorer (explorer.exe). 0%? That's because you're not doing anything with it. You're reading this web page.
I'm guessing that if I were running one of those "Ubuntu under Android" things that you can get for Android (I've never tried them as every device I've had had some kind of hardware issue preventing it from being likely to work, and the descriptions have always suggested they suck anyway...) I'd also see next to no increase in power usage, after starting it but not actually launching any X11 applications, despite that literally being an entire desktop operating system running on a phone, with all the components being in place.
So there really aren't any power implications when it comes to Microsoft shipping a full version of Windows for power saving devices, as long as - and they do - Microsoft includes a power efficient UI (Metro) for the tasks you'll be using the device for.
The only real reason for Microsoft not to ship their desktop OS on phones is that it takes up way too much disk space. As in "That 32G you get with an HP Stream 8 sounds sweet, but actually Windows takes up about around 20G of it, so get ready to buy an SD card straight away."
That really is it. I'm using that very device. Battery life is pretty ordinary for a tablet. I've seen much worse.