The central performance requirement for electrochemical energy storage systems for the full power-assist hybrid electric vehicle (HEV) is pulse power capability, typically 25-40 kW pulse power capability for 10 seconds duration. Standard test procedures utilize constant current pulses. However, in the HEV application, the power transient for acceleration is a ramped power transient and the power transient for regenerative braking power is a descending power ramp. This paper compares the usable power capability of batteries and supercapacitors under constant current, constant power, and ramped power transients. Although the usable battery discharge power is relatively insensitive to the transient type applied, 10-40% higher regenerative braking charge capability is observed with ramped power transients. With supercapacitors, the discharge and charge capability is much more strongly dependent on the type of power transient. The discharge power capability in a ramped power transient is 2.4 times that in a constant current pulse. The regen charge power capability is over 3 times that in a constant current pulse. Standard constant current test procedures thus underestimate the power capability of supercapacitors for HEV applications by several-fold. Supercapacitors provided over 2500 W/kg usable power for HEV applications, exceeding that of high power nickel metal hydride and lithium ion batteries tested.