Materials exhibiting insulator to metal transition (IMT) and transition metal oxides showing threshold switching behavior are considered as promising candidates for selector devices for crossbar non-volatile memory application. In this study, we use an electrothermal model to simulate the behavior of nanoscale selectors based on several different functional oxides (TaOx, VO2 and NbO2). We extract the device characteristics, such as threshold voltage (VTH), leakage current, device temperature in the ON state, and the size of the conductive filament as a function of selector diameter and functional layer thickness. In addition, we benchmark these devices in a 1 selector/1 resistor (1S1R) cell with a generic phase change-like memory element. These findings provide an insight into how device performance changes with scaling and help with material selection and design of selectors.