The dynamics of the ocean is shaped by complex interactions between physical processes across multiple scales. The submesoscale is particularly interesting due to its crucial role as path for dissipation of kinetic energy from large to small scales. However, the mechanisms that constitute this path, such as hydrodynamic instabilities, are not completely understood. Moreover, a recent study showed that anticyclonic submesoscale flows forced by a sudden change in surface wind stress develop what could be considered as a new submesoscale instability: the Ekman-Inertial Instability (EII), whose unique features make it capable of overcoming the effects of other common submesoscale processes. Using numerical simulations, this work investigates the similarities and differences between EII and the traditional Inertial Instability in a 2D submesoscale current. Our simulations show a much faster growth rate for EII, which results in a stronger vertical flow that is induced much earlier than the one observed in Inertial Instability and is capable of dissipating more kinetic energy. Both instabilities, however, seem to radiate internal waves away from the current. In addition, our results show that the flow takes almost the same time, from the onset of each instability, to return to a stable state. Finally, we explore how the intensity of the current affects the growth rate and total kinetic energy dissipation in each case.