Electronic stopping cross sections (SCSs) of nickel, silicon, and nickel-silicon alloys for protons and helium (He) ions are studied in the regime of medium- and low-energy ion scattering, i.e., for ion energies in the range from 500 eV to 200 keV. For protons, at velocities below the Bohr velocity the deduced SCS is proportional to the ion velocity for all investigated materials. In contrast, for He ions nonlinear velocity scaling is observed in all investigated materials. Static calculations using density functional theory (DFT) available from the literature accurately predict the SCS of Ni and Ni-Si alloy in the regime with observed velocity proportionality. At higher energies, the energy dependence of the deduced SCS of Ni for protons and He ions agrees with the prediction by recent time-dependent DFT calculations. The measured SCS of the Ni-Si alloy was compared to the SCS obtained from Bragg's rule based on SCS for Ni and Si deduced in this study, yielding good agreement for protons, but systematic deviations for He projectiles, by almost 20%. Overall, the obtained data indicate the importance of nonadiabatic processes such as charge exchange for proper modeling of electronic stopping of, in particular, medium-energy ions heavier than protons in solids.