  We compare the efficiency of four-wave mixing in quantum degenerate gases of
bosonic and fermionic atoms. It is shown that matter-wave gratings formed from
either bosonic or fermionic atoms can in principle exhibit nearly identical
Bragg-scattering, i.e. four-wave mixing, properties. This implies that effects
such as coherent matter-wave amplification and superradiance can occur in
degenerate fermi gases. While in the boson case the Bragg resonance is clearly
due to `Bose enhancement', in the case of fermions the resonance is due to
constructive many-particle quantum interference.
