  Compact binary system mergers are expected to generate gravitational
radiation detectable by ground-based interferometers. A subset of these, the
merger of a neutron star with another neutron star or a black hole, are also
the most popular model for the production of short gamma-ray bursts (GRBs). The
Swift Burst Alert Telescope (BAT) and the Fermi Gamma-ray Burst Monitor (GBM)
trigger on short GRBs (SGRBs) at rates that reflect their relative sky
exposures, with the BAT detecting 10 per year compared to about 45 for GBM. We
examine the SGRB populations detected by Swift BAT and Fermi GBM. We find that
the Swift BAT triggers on weaker SGRBs than Fermi GBM, providing they occur
close to the center of the BAT field-of-view, and that the Fermi GBM SGRB
detection threshold remains flatter across its field-of-view. Overall, these
effects combine to give the instruments the same average sensitivity, and
account for the SGRBs that trigger one instrument but not the other. We do not
find any evidence that the BAT and GBM are detecting significantly different
populations of SGRBs. Both instruments can detect untriggered SGRBs using
ground searches seeded with time and position. The detection of SGRBs below the
on-board triggering sensitivities of Swift BAT and Fermi GBM increases the
possibility of detecting and localizing the electromagnetic counterparts of
gravitational wave events seen by the new generation of gravitational wave
detectors.
