We analysed how the active galactic nucleus (AGN) X-ray primary continuum depends on AGN activity in radio, using the data of RXTE Spectral & Timing Database (Rossi X-ray Timing Explorer) and INTEGRAL (INTErnational Gamma-Ray Astrophysics Laboratory). Our aim is to test the relation between spectral shapes of these AGNs and the prediction of the spin-paradigm model of the AGN central engine. We have found that for the major part of radio-quiet (RQ) AGNs the value of high-energy exponential cut-off in primary spectrum appears to be significantly higher than 100 keV and thus follows the spin-paradigm predictions. In the same time, near 25% of radio-loud (RL) AGNs demonstrate the high-energy cut-off at the energies above 150 keV, contradicting the spin paradigm. We have composed a sample of peculiar 69 RQ and 10 RL AGNs that seem to contradict to the spin paradigm for further individual studies of these objects.