As was described by Anole, a GBOX counts both the rising and falling edges (e.g. closing and opening of a reed switch). If these edges are equally spaced (like a square wave), you get a doubling of resolution, but not necessarily accuracy. However if your positioner emits short pulses, the benefits might be nil because the counts occur at nearly the same pointing position. All of my positioners happen to exhibit square waves when I scope them. Actual accuracy also is affected by factors not related to the controller, including mechanical slop, backlash (different count for the same position, depending on the direction of approach) and overrun (how far the positioner moves after the controller cuts the power).
I started with one VBOX and one GBOX. I now have one VBOX and seven GBOXes. Go figure.