Average power, its why PWM dimming works on LEDs well, LEDs make a good strobe into Mhz , but to keep average power up you start dumping very large currents through them.
Big LEDs prefer to be current driven, the pulsing thing is a bit of red herring, PWM, a Philips Patent in the U.S., is used for dimming and for people who read pulsed lumens from the data sheet like a light meter not a human.
Cheers Adam