1GHz BeagleBone?
I think you mean 720MHz Mr Writer!
Both products are great in their own way, BeagleBone has a powerful general core with a NEON vector processor and lots of low-level I/O functionality that you'd normally have to use an intermediary chip for like PWM, ADC etc. The chip is commercially available and the design is simple and so easy to produce custom models. The unit is designed to be expanded.
RaspberryPi is cheap but difficult to reproduce for commercial purposes (cpu can only be purchased in whopping quantities and stacked memory is difficult to manufacture). On the other hand whilst the main CPU is a bit weak it has a very powerful graphics core + DSP and so some dedicated time on coding for it could yield surprising performance. Also has HDMI out. It's more of an Application processor like what you'd expect to find in a smartphone (was originally designed for camcorders).
Biting the hand that feeds IT
