Compared to conventional NAND flash resistive switching metal-oxide cells show a number of advantages, like an increased endurance, lower energy consumption, and superior switching speed. Understanding the role of defects for the resistive switching phenomenon in metal oxides is crucial for their improvement and thereby also for their acceptance as a next generation data storage device. Strontium titanate (STO) is considered a model material due to its thoroughly investigated defect chemistry. This paper presents a comparative study of the switching kinetics for three different compositions [Sr]/([Sr]+[Ti]) of 0.57 (Sr-rich), 0.50 (stoichiometric STO), and 0.46 (Ti-rich STO). The STO films, deposited by atomic layer deposition, were integrated in Pt/STO/TiN nanocrossbars with a feature size of 100 nm. By analysis of the transient currents, the switching kinetics are investigated between 10 ns and 104 s for the SET and 10 ns and 100 s for the RESET. A clear influence of the composition on the degree of nonlinearity of the switching kinetics was observed. Applying an analytical model for the oxygen vacancy migration, we were able to explain the differences in the SET kinetics by composition-dependent changes in the thermal conductivity and by a lower activation energy for the Ti-rich sample. This might be utilized in design rules of future ReRAM devices.