If you look in the BD instructions, they show the throw distance of light versus time on high and low. After 30 minutes the range on high has decreased from 70 meters down to 57 meters, and at 10 hours its about the same light as the low setting.
With fresh batteries, the light will run for 50 hours before being completely dead on high. 200 hours before completely dead on low.
Also, the 4x AAA batteries weigh 48g. Total weight 110g.
The H52 (assume standard model)is rated differently. Their ratings are how long the light will maintain a light output level before stepping down in power. So, you get a full 3 hours at 116 lumens (closest to BD light high level) before it even starts to dim. The single eneloop AA battery weighs only 12 grams. With single battery and headband you are at 80grams with the H52.
I have the H51, now obsolete. In the true dark, I can hike with the L1, which is 2.5 lumens. The similar level on the H52 (2.9 lumens) will run for 4 days, or about 100 hours, on 1 battery.
So, BD storm vs H52: At 0 hours, 3 hours the H52 is brighter. At 50 hours, maybe about the same. On a usable low, both run about 100 hours. The H52 is smaller and lighter by 30 grams. You can either bank the weight loss, or pack and extra 2 batteries for the H52. The zebralight lamps are truly great. The multiple AAA form factor is inefficient, lazy engineering. The single AA employs more expensive electronics to wring more power out of the cell, not to mention that AA batteries pack alot more juice for size and weight than a AAA.
Finally, you can put in some higher capacity lithium 14500 cells into the zebralight to really extend runtime or brightness. The glow in the dark headband for the zebralight is a nice touch too, I can typically see it for a few hours after going to bed.