Right now I don't have the funds for either of these lights, but if I had to pick one of the new L*D CE lights, it would not be the L1D. As others have said, the L0D attains an impressive brightness while maintaining a decent runtime on a very common (albeit slightly lesser value) cell whilst being unnoticable in a pocket. If you are that concerned about buying AAs rather than AAAs, use a NiMH.
The L2D remains small enough to be considered a compact handheld flashlight and has all of the nice features (like instant high/low, etc.) packed into the "full sized" model, while blowing the L0D out of the water on Turbo brightness.
The L1D is larger and bulkier than other 1AA lights, yet only manages to get approximately the same brightness as the L0D. It has a nicer interface, but it is still too big (IMHO) to EDC in a pocket. Therefore, since you have to carry in a bag or jacket pocket anyway, you might as well slap that extra battery in there and enjoy the extra brightness/runtime given by double the voltage and double the capacity.
For me, I'm not super keen on the design/UI of the L0D (I have an L0P SE) as it's kind of hard to activate one handed, not to mention change modes cleanly. Still, as far as being a virtually unoticable EDC powerhouse that runs on common batts, I can't think of a better choice. For a more "luxury" full-sized experience, I'd go with the L2D for reasons stated above.