The possibilities of using Kohn-Sham density functional theory to make accurate predictions of core photoelectron binding energies and chemical shifts are explored through a series of calculations on compounds of different sizes and types. The recent proposal of an ‘unrestricted generalized transition state’ (UGTS) method, for this purpose [D.P. Chong, Chem. Phys. Lett. 232 (1995) 486; D.P. Chong, J. Chem. Phys. 103 (1995) 1842], is put to test vs. full separate state optimizations of the ground and core hole states, that is a ‘ΔKohn-Sham’ (ΔKS) method. It is found that while internal parametrizations in terms of grid and basis set expansions can be well controlled there is still a notable dependency of the absolute binding energies on the choice of functional for both the UGTS and ΔKS methods. As for pure ab initio ΔSCF the former method must still be viewed as an approximation of the latter. Keeping these dependencies in mind, Kohn-Sham calculations seem to provide a promising tool for predicting binding energies and chemical shifts of an accuracy that approaches that of experiments.