We study radiative properties of hot accretion flows in a general relativistic model with an exact treatment of global Comptonization, developed in our recent works. We note a strong dependence of electron temperature on the strength of magnetic field and we clarify that the underlying mechanism involves the change of the flow structure, with more strongly magnetised flows approaching the slab geometry more closely. We find that the model with thermal synchrotron radiation being the main source of seed photons agrees with the spectral index vs Eddington ratio relation observed in black hole transients below 1 per cent of the Eddington luminosity, L Edd , and models with a weak direct heating of electrons (small δ) are more consistent with observations. Models with large δ predict slightly too soft spectra, furthermore, they strongly overpredict electron temperatures at ∼ 0.01L Edd . The low-luminosity spectra, at < ∼ 0.001L Edd , deviate from a power-law shape in the soft X-ray range and we note that the first-scattering bump often resembles a thermal like component, with the temperature of a few hundred eV, superimposed on a power-law spectrum. The model with thermal Comptonization of thermal synchrotron radiation does not agree with well studied AGNs observed below ∼ 0.01L Edd , for which there is a substantial evidence for the lack of an inner cold disc. This indicates that the model of hot flows powering AGNs should be revised, possibly by taking into account an additional (but internal to the flow) source of seed photons.