Both are referred to as "amp in a box" pedal types. The BE-OD in particular earns for itself the designation "BSIAB" or brown-sound-in-a-box.
I own the Friedman BE-OD and it's hands down the best overdrive/distortion pedal I've ever played.
The BE-OD is missing a midrange control, but the Dirty Shirley has a midrange pot. The BE-OD has a "tight" control pot, whereas the Dirty Shirley only has an on/off toggle for the tight control, used to tighten up the bottom end.
The concept of this built is to combine the two pedals into a single stomp-box enclosure with all the controls of both.
drilling template, center punched for pilot holes:
