Hello,
You can put higher current through the LED with pulses that's true, but the current only lasts for the pulse period unlike a constant current. That means the average current stays the same. The problem is, with higher current the LED becomes more inefficient, so pulsing an LED with an average current the same as a constant current actually does not appear as bright.
I proved this some time ago by making measurements like you are doing. The better way to measure the light output difference (if any) is to compare it to an LED that is driven with a constant current, since this is what we want to test anyway. You can use your eye to see any change in light output with the pulsed compared to the constant current driven LED. It helps to construct a comparative light brightness device that would help see the difference, but you can even see the difference by shining the pulsed LED on a white wall and the non pulsed LED on the same wall in another place.
Of course you want to make sure you start out with LEDs that are similar in character, so you test them both first with constant current. Then, to make sure the dynamics of both LED are the same after you do the first test you swap LEDs and repeat the test again and you had better get the same results.
My conclusion was that it's not easy to make the test but the results came out pretty much like the data sheet indicates...when the LED is driven harder the efficiency drops.
There are other reasons to pulse however which you may wish to look into.