Power density. A single CR123A cell is roughly equivalent to 2 AA cells (capacity and voltage). So basically it lets you have the performance of a 2xAA light shrunk down to smaller than a 1xAA light.
This was a big deal years ago but now a 1xAA light can be pretty competitive unless you really need 300+ lumens out of a single cell light. In that case, a CR123A or Li-ion secondary cell becomes necessary.
The amount of output you require for jogging at night depends on the amount of light already present where you are running. If your flashlight is the only source of light, then the correct level of output lets you see far enough ahead to make proper decisions and has enough spill to safely choose your footing. If there are other sources of lights (street lights, cars driving by with headlights, etc), then your eyes will be adapted to that and your flashlight will need to have a bright enough spill so that you can still place your foot safely even if the other lights cause your footing to be in shadow.
There are two common mistakes when jogging with a flashlight:
1. using the hot spot of the beam to see your footing. This utterly ruins your night vision and makes it difficult to see any distance even with the flashlight.
2. using too high an output. If your light is enough brighter than the ambient light that your eyes adapt to it, then it's too bright. You're sacrificing battery life and peripheral vision for no benefit.
Get yourself an inexpensive multi-mode light and take it running. You'll quickly figure out how low is too low.
--flatline
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