The zeroth-order regular approximation (ZORA) to the Dirac Hamiltonian and the Douglas-Kroll-Hess Hamiltonian (DKH) in their scalar-relativistic formulation have been implemented in a density functional code. The two approaches are compared on the same footing, i.e., using the same exchange-correlation functionals, basis sets and grids for numerical integration. The monohydrides, monooxides and monofluorides of La, Lu, Ac and Lr have been selected for a calibration study. Both methods yield very consistent results for bond lengths, binding energies and vibrational constants. Comparison is also made to experimental data as well as other relativistic all-electron and pseudopotential results.