For Pb-free 35B(2)O(3)35Bi(2)O(3)(30-x)TeO2(x)BaO (x=5, 10, 15, 20, and 25 mol%) and (90-x)TeO(2)10Bi(2)O(3)(x)BaO (x=10, 15, and 20 mol%) glass systems, gamma and neutron (both fast and thermal neutron) radiation shielding features were examined and compared. Within 0.015-15 MeV photon energy, mass attenuation coefficients (mu/rho), for all samples, which have been assessed using WinXCOM program are in fair agreement with deduced MCNP5 simulation code mu/rho results. For all selected samples, at the lowest energy, mu/rho has bigger values whereas at higher energy regions possess lower values. Furthermore, by employing mu/rho values, effective atomic number (Z(eff)), effective electron density (N-eff), half-value layer (HVL), tenth-value layer (TVL), and mean free path (MFP) are figured out for both glass systems. For studied samples, with the gradual replacement of TeO2 content with BaO, the derived values of Z(eff), HVL, TVL, and MFP revealed improved gamma -ray shielding potentiality. Besides, within photon energy range of 0.015-15 MeV, exposure build-up factors (EBFs) and energy absorption build-up factors (EABFs) were estimated for all samples by utilizing GP fitting method as a function of different penetration depths (0.5, 1, 2, 3, 4, 5, 6, 7, 8, 10, 15, 20, 25, 30, 35, and 40 mfp). The 35B(2)O(3)-35Bi(2)O(3)-5TeO(2)-25BaO (mol%) glass relatively larger mu/rho and Z(eff) values, lower HVL, TVL, and MFP values, and minimal EBF and EABF values confirm its superior gamma -ray attenuation competence among all samples. Additionally, in comparison, HVL and MFP values of 35B(2)O(3)-35Bi(2)O(3)-5TeO(2)-25BaO (mol%) sample are lower than the respective values of some commercial gamma -ray shielding glasses and different types of standard concretes, signifying its better shielding features than them. Moreover, macroscopic removal cross-section for fast neutrons (Sigma (R)), coherent scattering cross-section (sigma (cs)), incoherent scattering cross-section (sigma (ics)), absorption cross-section (sigma (A)), and total cross-section (sigma (T)) for thermal neutrons absorption were derived for both glass systems. Among all selected glasses, 35B(2)O(3)-35Bi(2)O(3)-5TeO(2)-25BaO (mol%) sample possesses relatively higher Sigma (R) (0.106 cm(-1)) and 'sigma (T)' (8.809 cm(-1) at 0.0253 eV neutron energy) values for fast and thermal neutrons attenuation, respectively, demonstrating its favorable absorption capability for neutrons.