I've followed the L0p discussion on cpf though I don't have one yet (I have an L1p which is similar but AA powered). I think the Arc makes more sense as an emergency light because of its much longer runtime. The L0p works pretty well on a NiMH cell or the somewhat rare L92 lithium AAA cell because of those cells' high current capability. It does rather terribly on a normal alkaline cell, with output dropping sharply after just a few minutes.
I think the L1p is a possible replacement for the Surefire G2's etc. that some people have in their kits. It's only about half as bright, but it runs for longer using a single, duff common AA cell, plus it's LED so no bulb to burn out, and the long dim "tail" as the battery poops out is still useful light (unlike an incandescent whose tail is mostly invisible infrared). The L0p is sort of a shrunken down L1p with lower output and a less-controlled beam shape because of the smaller reflector.
The L0p might make sense accompanying an Arc AAA (or a coin cell light) in a kit, if you want to also have a brighter light along, and you're trying to standardize on AAA cells for everything. (A Princeton Tec Rage is another possibility for a bright light). If you don't mind AA's and a larger light, I'd go for the L1p.
By the way I've been wanting to get around to posting an L1p review here since maybe the L1p isn't well enough known on ETS yet. It would be great if you beat me to it so I don't have to bother <img src="/images/graemlins/wink.gif" alt="" />.