Several comments: I have my doubts about some of the Brightstar claims, simply because they don't make a lot of sense. One of the reasons that AE light is rated for lower output should be obvious. If you want full output, you need to drive the light at roughly 24 watts. To get 110 minute runt time, that means about 50 watt hours from the battery.
If you look at the battery ratings, the AE light battery isn't anywhere near big enough for that. My guess is the lamp is being run at considerably less than 24 watts. I also doubt thatthe required 8 cells would fit in the packaging.
The problem cuts both ways. For the Brightstar light to offer both higher lumens and longer run times means bigger battery, and not a little bigger either. I have serious doubts that you can resell a 50w hour LiIon pack at retail for $70. You are going to need 8 1.5ah cells, and I don't think anyone can buy the cells, package them, distribute and resell them at $70 and even come close to breaking even.
My gut feel is the lumen output on the Brightstar is based upon the lamp, rather than the 'total package' or any actual measurement. I.E. it could deliver the rated output, but not with supplied battery pack/ballast/reflector and claimed run time.
I would also add that AE has apparently begun production shipments of their product.
At the end of the day I suspect there isn't going to be a lot of difference in either output or run time on these products.
My thoughts.