Model-Independent Comparison of Direct versus Indirect Detection of Supersymmetric Dark Matter

We compare the rate for scattering of neutralinos from nuclei with the flux of muons induced by energetic neutrinos from neutralino annihilation in the Sun and Earth. We consider scalar and spin interactions of neutralinos. We find that the event rate in a kg of Ge is roughly equivalent to that in a 1${0}^{5}$--1${0}^{7}$-${\mathrm{m}}^{2}$ muon detector for a neutralino with primarily scalar coupling to nuclei. For a spin-coupled neutralino, the event rate in a 50-g H detector is roughly that in a 10--500-${\mathrm{m}}^{2}$ muon detector. Expected backgrounds favor forthcoming elastic-scattering detectors for scalar couplings while neutrino detectors are favored for spin couplings.