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We present a comparative analysis of spectral properties of Black Hole (BH) and Neutron Star (NS) X-ray binaries during transition events observed with BeppoSAX and RXTE satellites. In particular, we investigated the behavior of Comptonized component of X-ray spectra when object evolves from the low to high spectral states. The basic models to fit X-ray spectra of these objects are upscattering models (so called BMC and COMPTB models) which are the first principal models. These models taking into account both dynamical and thermal Comptonization and allow to study separate contributions of thermal component and Comptonization component (bulk and thermal effect of Comptonization processes). Specifically, we tested quite a few observations of BHs (GRS 1915+105, 4U1630-47 and SS 433) and NSs (4U 1728-34, 4U 1820-30, Sco X-1, GX 340-0 and GX 3+1) applying BMC and COMPTB models. In this way it was found a crucial difference in behavior of photon index vs mass accretion rate (mdot) for BHs and NSs. Namely, we revealed the stability of the photon index around typical value of Gamma=2 versus mdot (or electron temperature) during spectral evolution of NS sources. We also detected the new index reduction phase detected over the FB in Sco X-1 for the hard Comptonized component near the Eddington regime. This intrinsic property of NS is fundamentally different from that in BH binary sources for which the index demonstrates monotonic growth with mass accretion rate followed by its saturation at high values of mdot. These index-mass accretion rate behavior during X-ray spectral transition events can be considered as signatures, which allow to differ NS from BH.