Despite the massive increase of renewable energy generation in Greece, large-scale battery energy storage systems (BESS) are yet to be integrated in the Greek electricity market. This paper analyzes the profitability of BESS in Greece, focusing on the Day-Ahead Market (DAM) and the Frequency Containment Reserve (FCR) market. To this end, we examine and compare the following three instances of BESS market participation with respect to the short-term uncertainty BESS participants face in terms of market prices and FCR utilization factors: (a) a theoretical perfect information instance, (b) a deterministic instance based on average historical values of the uncertain parameters, and (c) a stochastic instance based on alternative scenarios stemming from historical data. The last two instances are complemented by an out-of-sample validation representing BESS operation after uncertainty is materialized. Furthermore, for each of these three instances, we explore three cases involving participation only in the DAM, only in the FCR market, and in a combination of the DAM and FCR market, accounting for the different pricing mechanisms of these markets. The case studies employ real market and frequency data from Greece and compare the three instances and three market participation cases in terms of achieved profit and energy violation rate.