In this paper, we propose an advanced Levelised Cost of Storage (LCOS) model to compare electricity and thermal energy storage for cooling applications. The proposed model is applied to evaluate the LCOS for Lithium-Ion (Li-Ion) battery, chilled water and ice storage for Photovoltaic (PV) powered cooling for an office, a hotel, and a refrigerated warehouse scenario in Singapore. Parametric energy simulations varying the storage size were carried out to analyse the optimal storage size for different applications and technologies. The thermal energy storages were found to cause a lower chiller plant Coefficient of Performance (COP), which leads to an increased energy consumption. As a result, the battery can achieve a better performance in terms of self-sufficiency. The LCOS for the thermal energy storages are generally lower than that of the battery, at 23-47 USD ct/kWh(el) for all the analysed storage sizes. However, a well-sized battery can only achieve LCOS of 55 USD ct/kWh(el) for the office scenario, 71 USD ct/kWh(el) for the hotel scenario, and 55 USD ct/kWh(el) for the refrigerated warehouse, due to high investment cost. This work also highlights that thermal energy storage has a better potential for applications that require a larger shift of energy, such as in the investigated hotel and refrigerated warehouse scenario.