Not enough information given in the original question.
We need to know the frequency of the square wave. For instance, if the frequency were 1 Hz, it's obvious that the second LED would be much brighter half the time and much darker half the time. At least until the LED failed from overcurrent, then it would be much darker all the time.
We also need to know viewing angle. You'll find that your peripheral vision performs differently than your direct vision, due to the different distribution of rods and cones. Rods react much faster than cones and are more light sensitive, while cones are slower and see color, so that ties into the frequency question again. Ever notice that you can sometimes detect monitor flicker when you aren't looking right at the monitor?
In the general sense, at a high enough frequency to achieve fusion, I'd say the PWM LED would appear brighter. Reducing the ON time of an LED is a common technique to save power. In the extreme case, it can save components as well by eliminating the resistor.
But a little empirical testing wouldn't hurt you. It's a pretty trivial experiment after all.
Sorry, I though it obvious that I would have to get over the 24 Hz. flicker frequency to avoid the persistence of vision obstacle. Let's say that you have your choice of any frequency from 25 Hz. to daylight.
Viewing angle is dead on boresight.
Empirical testing to follow. It is a trivial experiment and one that I probably should have done instead of asking the question if anybody has done the experiment and how did it turn out?
Let me pose the question for what I **REALLY** want to know.
I've got a white landing light of about twenty watts (DC power). I shine the light at the ground when I'm about 350' AGL. It lights a rough ellipse on the ground and lets me see whether or not there are animals on the runway before I collide with them.
I run the light on DC and get a particular illumination. If I run the same exact device on AC of any frequency you want above the flicker level and I adjust the current so that the pulse width times the current gives me the same power into the light, will the light appear brighter to me as reflected from the SAME ground at the SAME altitude at the SAME attitude, at the SAME .... In other words, the only differences is pulsed power versus DC. Does the pulse width affect the result (right up to the maximum pulse current of the device)? Is it any brighter at any combination of pulse width and current than at DC?
THat should take care of any test conditions, I hope.
Jim