The four-component matrix Dirac-Kohn-Sham (mDKS) implementation of EPR g- and hyperfine A-tensor calculations within a restricted kinetic balance framework in the ReSpect code has been extended to hybrid functionals. The methodology is validated for an extended set of small 4d(1) and 5d(1) [MEXn](q) systems, and for a series of larger Ir(II) and Pt(III) d7 complexes (S = 1/2) with particularly large g-tensor anisotropies. Different density functionals (PBE, BP86, B3LYP-xHF, PBE0-xHF) with variable exact-exchange admixture x (ranging from 0% to 50%) have been evaluated, and the influence of structure and basis set has been examined. Notably, hybrid functionals with an exact-exchange admixture of about 40% provide the best agreement with experiment and clearly outperform the generalized-gradient approximation (GGA) functionals, in particular for the hyperfine couplings. Comparison with computations at the one-component second-order perturbational level within the Douglas-Kroll-Hess framework (1c-DKH), and a scaling of the speed of light at the four-component mDKS level, provide insight into the importance of higher-order relativistic effects for both properties. In the more extreme cases of some iridium(II) and platinum(III) complexes, the widely used leading-order perturbational treatment of SO effects in EPR calculations fails to reproduce not only the magnitude but also the sign of certain g-shift components (with the contribution of higher-order SO effects amounting to several hundreds of ppt in 5d complexes). The four-component hybrid mDKS calculations perform very well, giving overall good agreement with the experimental data.