This study evaluates the thermodynamic performance of the following two CO₂ liquefaction processes for onboard carbon capture and storage (OCCS) on a 174,000 m³ LNG carrier: the Linde–Hampson and vapor compression refrigeration cycles. The cycles were designed based on realistic vessel operating conditions and compared using the specific energy consumption (SEC) as the primary performance indicator, alongside the coefficient of performance (COP). To enable a fair comparison of the two distinct cycles, a complementary COP metric was validated for the open-loop Linde–Hampson cycle by establishing a system-level definition of heat removal. The validity of this metric was confirmed by demonstrating that its optimal point (maximum COP) aligns with that of the primary metric (minimum SEC), ensuring thermodynamic consistency. The analysis reveals that the vapor compression cycle demonstrates superior performance, achieving an 8.35% higher COP and an 11.45% lower SEC than the Linde–Hampson cycle. This work provides a consistent methodology for the comparative assessment of open- and closed-loop liquefaction systems.