For Pb-free 35B2O3‒35Bi2O3‒(30–x)TeO2‒(x)BaO (x = 5, 10, 15, 20, and 25 mol%) and (90–x)TeO2‒10Bi2O3‒(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 (μ/ρ), for all samples, which have been assessed using WinXCOM program are in fair agreement with deduced MCNP5 simulation code μ/ρ results. For all selected samples, at the lowest energy, μ/ρ has bigger values whereas at higher energy regions possess lower values. Furthermore, by employing μ/ρ values, effective atomic number (Zeff), effective electron density (Neff), 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 Zeff, HVL, TVL, and MFP revealed improved γ-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 G‒P 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 35B2O3–35Bi2O3–5TeO2–25BaO (mol%) glass relatively larger μ/ρ and Zeff values, lower HVL, TVL, and MFP values, and minimal EBF and EABF values confirm its superior γ-ray attenuation competence among all samples. Additionally, in comparison, HVL and MFP values of 35B2O3–35Bi2O3–5TeO2–25BaO (mol%) sample are lower than the respective values of some commercial γ-ray shielding glasses and different types of standard concretes, signifying its better shielding features than them. Moreover, macroscopic removal cross-section for fast neutrons (ΣR), coherent scattering cross-section (σcs), incoherent scattering cross-section (σics), absorption cross-section (σA), and total cross-section (σT) for thermal neutrons absorption were derived for both glass systems. Among all selected glasses, 35B2O3–35Bi2O3–5TeO2–25BaO (mol%) sample possesses relatively higher ΣR (0.106 cm−1) and ‘σT’ (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.