The BeagleBone is an easy to use microprocessor breakout project board. Much like the Raspberry Pi, it allows your to run an embedded Linux kernel to execute all kinds of processing in the context of a standalone project.
According to this thorough article comparing the two boards, the BeagleBone is twice as fast as the Raspberry Pi for the same cost. However, the Raspberry Pi has better audio and video capabilities.
Extensibility is also a big factor. BeagleBone has “Capes” and Raspberry Pi extends using an add-on that allows you to use all the Arduino Shields. You’ll need to extend the BeagleBone to gain audio and video features comparable to the Pi.