The L0p is considerably larger than an Arc AAA, has much less runtime, has slightly inferior (but not terrible) build quality if the L1p is representative, but is quite a bit brighter than the Arc, should have much more neutral color, and should have a nicer beam because of the reflector. Yes, 5.5 lumen minimum means an AAA premium v4 has guaranteed 5.5 lumens or better output on a fresh battery, probably more like 7 lumens. L0p output should be in the 16 lumen range, again based on L1p measurements. (Fenix, like some other manufacturers but unlike Arc and Surefire, does its lumen specs at the LED die rather than measuring what actually comes out of the flashlight after all internal losses).
My feeling is the lights serve distinct purposes. The Arc AAA is a long-running EDC bright enough for most close range uses and which carries ok on a keychain. The Fenix L1p is a pocket light that's quite powerful for its size (by mass market standards) and which can illuminate over fairly long distances and which works well on the ubiqitous and powerful AA NiMH cells. The L0p is a cross between the two, combining both the advantages and the disadvantages of both. I'm fond of my L1p and my two Arc AAA's but I don't plan to order an L0p right away. I think the L0p is a little too large and too special-purpose to carry on a keychain, and if I'm going to drop a light in my pocket, I don't mind the L1p's size.