Current usage was measured using an INA219 breakout connected to an Arduino and measuring the current drawn to each board's 5V input (either through a barrel jack or USB micro B connector).
Each board was connected to a minimum of peripherals during the test. The Beaglebone Black, Raspberry Pi model B, and Intel Galileo were connected only to a network through their ethernet port. The Arduino Yun was connected to a network through WiFi. The Raspberry Pi model A was not connected to a network, and instead connected to a USB keyboard and HDMI monitor.
Both the Beaglebone Black and Raspberry Pi model B have similar power usage under load, but the Beaglebone Black is noticeably lower at idle. Even with its greater performance in the benchmark, the Beaglebone Black is slightly better at power usage than the Raspberry Pi model B.
Finally, it's interesting to see the impact of WiFi with the Arduino Yun results. While running over WiFi the Yun demonstrated low power usage compared to the other boards. To see how running other boards with WiFi would compare, I ran a quick test to measure the power consumption of the Raspberry Pi model A board at idle and under load with a small USB WiFi adapter connected. Power usage with the WiFi adapter increased by about 30-150mA, depending on network activity, which puts it in line with the Arduino Yun results. In general running a board with WiFi doesn't appear to be a dramatic cost in power usage.