In the case of low-mass X-ray binaries, the companion star is often too faint for detection; therefore, there is no chance for dynamical studies to independently determine the mass of the compact object. In the absence of a mass estimate, one cannot make a distinction as to whether the binary hosts a black hole or neutron star. Therefore, the question arises whether this distinction can be made based on the X-ray data alone, even when there are no bursts or pulsations. These would automatically imply a neutron star, but they are not always present. Black hole systems are known to emit radiation with an unbroken power–law shape up to several hundred keV energies in their high/soft states. If the non-thermal Comptonization processes that are responsible for this are somehow related to the lack of a solid surface, and to the fact that more gravitational potential energy can be released for a black hole, then there would be a definite method to reliably distinguish between the two sources. This work intends to review the available observations and studies to compare how these two populations behave during their different spectral states. A conclusion can be made that high/soft-state spectra are really different for black holes and neutron stars, for the low/hard state; however, the same conclusion cannot be safely made.