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We fit hydrogen atmosphere models to the X-ray data for four neutron stars(three from a previous paper, plus 4U 2129+47) and six black hole candidates(A0620-00, GS 2000+25, GS 1124-68, GS 2023+33, GRO J1655-40, and GRO J0422+32).While the neutron stars are similar in their intrinsic X-ray spectra (similareffective temperatures and emission area radii ~10 km), the spectra of twoblack hole candidates are significantly different, and the spectra of theremaining four are consistent with a very large parameter space that includesthe neutron stars. The spectral differences between the neutron stars and blackhole candidates favors the interpretation that the quiescent neutron staremission is predominantly thermal emission from the neutron star surface. Ourwork suggests that an X-ray spectral comparison in quiescence provides anadditional means for distinguishing between neutron stars and black holes. Thefaint X-ray sources in globular clusters are also a class of objects which canbe investigated in this manner.Comment: 33 pages, including 3 ps figures, LaTeX. To appear in Ap

A Method for Distinguishing between Transiently Accreting Neutron Stars and Black Holes, in Quiescence