Another advantage that GGT (or DS) may have over PBFS is that the chunk splittings that each min-cut corresponds to is in a sense optimal: it is the best improvement to the diagram possible, when considering only steps that subdivide a single chunk in two. PBFS doesn’t have this, as it finds the breakpoints in order.
If the way this gets implemented is by aborting the computation as soon as a time/work threshold is exceeded, for GGT this probably means a better/fairer partial solution than PBFS (which may have spent all its time on the first chunk, and nother further).