The finite-time thermodynamic performance of steady flow Carnot and Brayton heat pump cycles has been studied for both finite and infinite thermal capacitance rates of heat reservoirs. The fundamental optimal relations of the two cycles are obtained. A comparison of the performance characteristics of the two cycles for the same boundary conditions (i.e. same heat source/sink inlet temperatures, thermal capacitance rates, and heat exchanger conductances) is shown. The effects of finite thermal capacitance rates of the working fluid and heat reservoirs and of the internal irreversibilities of the cycles on cycle performance are analyzed. Optimal matching between the temperatures of the working fluid and heat reservoirs is discussed.