I'm posting this from a Gigabyte Brix J1900 unit, and I have to say, I really like it. It's faster than I thought it would be, although I would hesitate to actually call it "fast".
It's the desktop J1900 Atom Bay Trail-D quad-core, which is clocked a bit faster than your usual Z3735F tablet Atom, and runs 64-bit OSes (no 32-bit UEFI shenanigans).
According to CPU-Z, it runs at 2415Mhz full-tilt (and stays boosted, it has a small fan inside), and according to RealTemp (ancient program), it's running at 2000Mhz (not accounting for "Burst" speeds?).
Either way, it's fast enough for web browsing, haven't done much media-watching with it yet. Some YouTube played OK.
Had some issues loading Linux Mint 17.3 Cinnamon 64-bit on it. Initially, it installed (although I had to plug in a USB Wifi adapter that works with Linux, as the onboard cuts out after like 2 minutes, like clockwork). But I had several "Freeze" issues. I tried updating the kernel to the newest available in Mint's Updater, 4.4-22, and it still froze up, so I decided to install Windows 7.
That went fine, and it seems to run OK on Windows 7. (There's a newer video driver from Intel, 4425, that works with these systems, compared to the drivers on the disc that came with the unit.) (win64_153343.4425)
However, on one of the units, I had forgotten to change the default behavior of the power-management, which is set to sleep the PC after 30 minutes. When I came back to the PC, after a while, I turned on my HDTV monitor, and moved and clicked the mouse, and I was greeted by a BIOS sign-on screen, and a Windows screen that said it hadn't started correctly. So it didn't come out of sleep right. Don't know why.
So I've disabled sleep.
I'm also running Folding@Home on the CPU (3 cores out of 4, apparently, by default), and I'm getting like 600PPD, and temps are (according to RealTemp) ~50C, at 100% CPU load. Not bad at all, really, especially since it stays at max "Burst" clock too, according to CPU-Z.
So I'm pretty happy with the purchase, and I'm sure it's very power-efficient to boot, although the size factor was the most important factor in my purchase, not the power efficiency.