Recently, models for Advection Dominated Accretion Flow (ADAF) have been shown to explain many of the quiescent properties of the X-ray and optical emission from black hole soft X-ray transients (BH SXT) (Narayan, McClintock and Yi 1996 ApJ 457, 821; Narayan, Barret and McClintock 1996, submitted to ApJ). One novel feature of the ADAF model is that the black hole event horizon plays a key role in the energetics of the flow, in that it absorbs the majority of the energy in the accretion flow. An ADAF flow around a neutron star (NS) SXT instead will release all of its accretion energy upon impacting on the NS surface (Yi et al 1996, submitted to A&A). Therefore one expects that NS SXT will be substantially more luminous than BH SXT in quiescence. We present results on 5 NS SXT and 4 BH SXT that appear to bear out this expectation. In the context of the ADAF model, the larger dynamic range in BH SXT outburst/quiescent luminosities can be seen as evidence for the existence of an event horizon in these BH.