While I am a major fan of the Raspberry Pi, I do at times find its limited GPIO availability somewhat of a letdown - this is where the BeagleBone Black really steps up and shines. With a total of 96 GPIO pins, there is enough I/O to connect anything one might need for a robotics project, lighting sequencer, or even a web server. With the ability to run Linux, Android, and many other operating systems, the BeagleBone Black makes for a formidable and flexible micro-PC. Its processor is more powerful than the Raspberry Pi, and its 2GB of on-board NAND flash makes it a clear winner in terms of storage flexibility.
Unfortunately with a limited resolution of just 1280x1024, the Raspberry Pi wins the battle for best micro-PC to use as a media streaming device. The Black is also lacking in terms of an analogue audio out port, as well as the built-in camera bus featured on the Pi. Honestly though, I do not know if these are major issues or not, as there are many "Capes" on the market that can easily add this functionality to the Black.
If you are not worried about video resolution, cameras, or analogue audio, and care more about how much processing power the board has, then the BeagleBone Black is the superior choice. As I mentioned, the 96 GPIO pins weigh heavily as the boards most attractive feature, as does its established Cape expansion board support. There are hundreds of Capes on the market that can be adapted to do just about anything an enterprising maker can think of.
While there are dedicated accessories in abundance for the Raspberry Pi and Arduino Due boards, the BeagleBone Black is beginning to see its accessory market grow. Logic Supply makes an excellent all metal chassis for the Black that is powder coated black or orange, and allows you to completely enclose the board in a robust case that will prevent damage and theft if mounted using the supplied mounting points.
Best of all, this case costs just $15 and fits the Black perfectly. Additionally, educational books such as "Bad to the Bone," by Steven F. Barrett and Jason Kridner, which is one of the best written development board books I have ever read.
Until the Raspberry Pi Foundation releases the next generation Raspberry Pi, I am going to have to declare the BeagleBone Black the winner by a very small margin in the micro-PC wars. When you break it down, each board has its purpose, and with them being cheap enough, ($45 for the BeagleBone Black, and $35 for the Raspberry Pi Model B), you can keep several of them on your workbench for prototyping, developing, and general use.
I have six Raspberry Pi boards now and will be picking up a few more BeagleBone Blacks in the coming weeks for an upcoming project.