We search the literature for reports on the spectral properties of neutron-star low-mass X-ray binaries when they have accretion luminosities between 1E34 and 1E36 ergs/s. We found that in this luminosity range the photon index (obtained from fitting a simple absorbed power-law in the 0.5-10 keV range) increases with decreasing 0.5-10 keV X-ray luminosity (i.e., the spectrum softens). Such behaviour has been reported before for individual sources, but here we demonstrate that very likely most (if not all) neutron-star systems behave in a similar manner and possibly even follow a universal relation. When comparing the neutron-star systems with black-hole systems, it is clear that most black-hole binaries have significantly harder spectra at luminosities of 1E34 - 1E35 erg/s. Despite a limited number of data points, there are indications that these spectral differences also extend to the 1E35 - 1E36 erg/s range. This observed difference between the neutron-star binaries and black-hole ones suggests that the spectral properties (between 0.5-10 keV) at 1E34 - 1E35 erg/s can be used to tentatively determine the nature of the accretor in unclassified X-ray binaries. We discuss our results in the context of properties of the accretion flow at low luminosities and we suggest that the observed spectral differences likely arise from the neutron-star surface becoming dominantly visible in the X-ray spectra. We also suggest that both the thermal component and the non-thermal component might be caused by low-level accretion onto the neutron-star surface for luminosities below a few times 1E34 erg/s.
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