  We compare the rate for elastic scattering of neutralinos from various nuclei
with the flux of upward muons induced by energetic neutrinos from neutralino
annihilation in the Sun and Earth. We consider both scalar and axial-vector
interactions of neutralinos with nuclei. We find that the event rate in a kg of
germanium is roughly equivalent to that in a $10^5$- to $10^7$-m$^2$ muon
detector for a neutralino with primarily scalar coupling to nuclei. For an
axially coupled neutralino, the event rate in a 50-gram hydrogen detector is
roughly the same as that in a 10- to 500-m$^2$ muon detector. Expected
experimental backgrounds favor forthcoming elastic-scattering detectors for
scalar couplings while the neutrino detectors have the advantage for
axial-vector couplings.
