200fr,
As the owner of both a AAA-LE and a LSH-S, I find myself EDC'ing, exclusively, the AAA simply based on size.
Wxcept when wargaming, I like my everyday stuff to fit in my pockets. All of my folding knives have low-lying pocket clips, my cell's small enough tp slip into my pocket,and even my keychain doesn't present as a big lump in my pants.
And that's my biggest issue with the LS -- it will present as a buldge -- it's like carrying a roll of pennies or "LifeSaver's" candy in one's pocket.
I carry the LS when I specifically have a potential need for it in-mind. It's got a lot more usable light than the AAA, but you will have to pay for this in size.
From the looks of your criteria, it seems that either of the two lights would be OK -- keep in mind this ancillary factor.
Allen
aka DumboRAT