As power systems continue to achieve higher penetrations of non-synchronous Renewable Energy (RE) sources, via replacement of conventional synchronous generators, the power system inertia reduces. Thus, the frequency stability of these power systems is challenged. This can be addressed by technologies such as flywheels, supercapacitors, and Battery Energy Storage Systems (BESSs). This paper discusses the application of Grid-following (GFL) and Grid-forming (GFM) BESS for frequency control in power systems with high RE penetration. MATLAB/Simulink is used to build a simple Australian interconnected power system model, and simulations are carried out at various RE penetrations in the power system. Simulation results show that the response parameters of GFL-BESS, such as deadband and power response time constant, significantly influence the dynamic performance and stability characteristics difference between GFL and GFM-BESS. By appropriately selecting the GFL and GFM operational parameters, required BESS capacity to maintain frequency within normal operating limits and the dynamic performance and stability characteristics differences can be reduced. Compared to GFL, using GFM would still be beneficial for low-inertia power systems, as using GFM based solution can reduce the BESS capacity required to maintain frequency stability by providing additional damping to the system.