Wow...so much to cover..and so many landmines to step on.
I don;t feel like loosing a leg today, so I'll add this:
In short, circuitry increases efficiency of an LED for a couple of basic reasons (not exhaustive here guys-no grenades please)-
1. circuitry allows the output of the LED to be regulated which not only determines run-time but also an ancillary causal bi-product- HEAT
The more that heat can be regulated (through, heat sinks, or whatever) the more efficient the LED can draw upon its source to output more efficiently form the demanded "load".
This believe it or not, is one of the reasons that flashlights have a certain amount of lumens. Many times the desired lumens output is determined by how much heat the unit wants to be limited to. This is because heat kills battery life.
To come round the mine field full circle now, circuitry is but one way( and not a bad way mind you) of how to help in this arena.
Cree LED are a quality diode in that they work well with circuitry, respond well to current draw (some diodes don't like current-what does "don't like" mean? it could mean it blows up, burns up, kills the battery, short circuits the system and a few other things).
I digressed here a bit, in the musings of my geek head, so sorry.
David
p.s. Hmmm I still have my legs for the moment