I measured my VIA-C7 at the plug at 27 watts including 2 hard drives. With the SHA256 instruction support (I added) in bitcoin it gets 1430 khash/s @1.8 GHz so it seems like a pretty good improvement in power efficiency.
The code has improved since my previous post, and my machine now gets about 1800 khash/s at 50 W. Nevertheless, Via C7 remains more efficient. In fact, I am considering getting a Via Nano motherboard, there is even a Mini-ITX model with a full PCIe slot.
The C7 version of bitcoin should work well on the Nano even if it is just a 32 bit mode, not 64. You might recompile it for 64 bit on a Nano and see if it still works right.