Unlike many other semiconductor devices with very thin separations between die layers, or sometimes tiny wires connecting contact points, LED construction is electro-mechanically more robust. While it is possible to cause arching on the substrate with higher voltage levels, the maximum power rating of an LED is mostly dependent on how hot it gets. That's the reason a good heatsink will cause an LED to have a substantially longer useful life when being continuously run at high power levels.
High power pulses of low duty cycle will add up to a much lower average heating level than those of a higher duty cycle, so the device runs cooler. Within reason, the "instantaneous peak" power, (not the "continuous running" power an LED can be run at) is just limited to how much of a pulse shock the device can withstand, (often quite a lot) as long as the pulse duration is short enough and the duty cycle is low enough to keep the device from overheating.
But that is only useful for special purpose apps, such as communications or burning holes in things. For lighting, just stick to the average continuous current rating, and make sure the device has at least the prescribed bit of heatsinking.