The BBB and the Raspberry Pi are designed to be relatively high-power (both computational, and power draw from DC) devices running a true multiuser OS.
This thing is more akin to an Arduino Micro or a Teensy - a low-power controller that could run a very long time on a tiny battery, no OS to speak of, just a single loop of essentially real-time code.
I just made a hardware clock for my PC (7-segment LED display mounted in a CD-ROM bay slot). I used an Arduino Micro to drive the display.
I may build a dedicated media server at home. A RasPi or BBB would be perfect.
I'm thinking to launch a stratospheric balloon. I need something to hold together and drive a GPS sensor, temperature sensor, VGA camera, SD card, and radio transmitter. Total weight and power consumption are severely limited. An Arduino or Teensy would be great.
Do a wall-mount big LCD screen at the office, showing the vital stats of our website in real time, for all to see? A RasPi or BBB.
Or you could go even more bare-metal and do everything with an AVR that costs $1 and a few components that you recover from the last floor sweep, like this:
http://florin.myip.org/blog/how-make-halloween-creepy-blinki...
See the differences? Horses for courses.