Different approaches are compared for relativistic density functional theory (DFT) and Hartree-Fock (HF) calculations of electron-nucleus hyperfine coupling (HFC) in molecules with light atoms, in transition metal complexes, and in selected actinide halide complexes with a formal metal 5f(1) configuration. The comparison includes hybrid density functionals with range-separated exchange. Within the variationally stable zeroth-order regular approximation (ZORA) relativistic framework, the HFC is obtained (i) with a linear response (LR) method where spin-orbit (SO) coupling is treated as a linear perturbation, (ii) with a spin-polarized approach closely related to a DFT method for calculating magnetic anisotropy (MA) previously devised by van Wüllen et al. where SO coupling is included variationally, (iii) with a quasi-restricted variational SO method previously devised by van Lenthe, van der Avoird, and Wormer (LWA). The MA and LWA approaches for HFC calculations were implemented in the open-source NWChem quantum chemistry package as part of this study. The methodology extends recent implementations for calculations of electronic g-factors (J. Chem. Theor. Comput.2013, 9, 1052). The impact of electron correlation (DFT vs HF) and DFT delocalization errors, the effects of spin-polarization, the importance of treating spin-orbit coupling beyond first-order, and the magnitude of finite-nucleus effects, are investigated. Similar to calculations of g-factors, the MA approach in conjunction with hybrid functionals performs reasonably well for theoretical predictions of HFC in a wide range of scenarios.