The bright LEDs such *do* put out a lot more power than the Laser Flare, perhaps 250 mW of optical power vs. no more than 5 mW for the laser.
The problem is that an LED spreads that power out over all the colors instead of just the one (green) the eye sees best, and the power is spread out over a much large beam, that gets larger much faster than a laser beam.
(a Fenix and such has a beam that starts out perhaps 100x larger than a laser and it goes downhill from there - even at the start with a 50x power advantage the LED is weaker per unit area. A handheld HID might emit several watts of optical power, perhaps 1000x a laser's power, but again the beam would start out 5000x or more larger)
The Flare's beam is a very thin line that gets thicker and longer very slowly with distance. If you shine a flashlight at a wall 10' away the beam is already significantly larger than it was at the exit of the flashlight. When you project the flashlight's spot size out to a distance of several miles it's trying to fill an area vastly large than the laser's area, which won't have grown nearly as much.
I don't think it's possible to aim a laser by hand at a target over a mile away. The laser spot is so small that no hand is steady enough, not to mention that you can't see where the beam is going when trying to hit an airplane (there's nothing to reflect a miss back at you). At best I suspect you try to sweep the Flare's line back and forth over the aircraft, knowing you'll hit it at some point.