Recent developments of the sources of intense and ultrashort x-ray pulses stimulate theoretical studies of phenomena occurring on ultrafast timescales. In the present study, spin-flip dynamics in transition metal complexes triggered by sub-femtosecond x-ray pulses are addressed theoretically using a density matrix-based time-dependent configuration interaction approach. The influence of different central metal ions and ligands on the character and efficiency of spin-flip dynamics is put in focus. According to our results, slight variations in the coordination sphere do not lead to qualitative differences in dynamics, whereas the nature of the central ion is more critical. However, the behavior in a row of transition metals demonstrates trends that are not consistent with general expectations. Thus, the peculiarities of spin dynamics have to be analyzed on a case-by-case basis.