The cryptocurrency market has attracted considerable attention from investors and researchers alike. This paper examines the volatility patterns of two major cryptocurrencies utilizing GARCH modeling: Bitcoin, based on a proof-of-work mechanism, and Cardano, operating on a proof-of-stake mechanism. Our findings reveal differences in the volatility structures of the two cryptocurrencies, with Cardano demonstrating a reduced long-term volatility compared to Bitcoin. This study suggests that transitioning from proof-of-work to proof-of-stake mechanisms might lead to a decrease in market volatility.