The best EDC light is the one you have with you when you need it
Since I am biased (and just blew $161 on a FF-III with spare chargers/batteries) I would say an at least two output level single cell LED light so it can be attached to your keychain, dropped in your pocket or a tiny holster.
The high/low output options allow for long runtimes if needed in an emergency and decent punch if you need to see what is out there. At the minimum, a keychain light with decent runtime since it is generally always with you is decent.
Although I have been keychain EDC'ing a AAA light around for the last 3.5 years I am switching (the horror!) My wife bought me a DSpeck Fire~Fly III for my birthday present with three RCR123A lithium-ion batteries and two chargers. Battery in the light, spare charger/battery combo at home and work to keep it fed. Swap out the RCR123 battery once a week or, if I plan on going somewere, swap on Monday and swap on Friday night for the weekend.
Why the FF-III? Simple, the batteries can be topped off without degrading performance so I'll never be caught with a dead battery. I'll program the high level high enough to get decent light output at least an hour/hour and a half of runtime and cool operation. The max level is for short term use to see what is out there. The low level is to walk around the house at night or get dressed in the morning without waking up my wife. I like the twisty operation since it will not break or get activated by whatever is in my pocket. When I go back to the desert, it will be reprogrammed for a lower low level and a slightly lower high level to handle the increased ambient temperatures. It will be lanyard mounted and be on me 24/7 with one charger/battery at work and the other charger/battery by my bunk. A few dozen CR123A primaries spread around in case I get stuck in a situation that needs extended runtimes. The primaries will be carried in a holster.
That is just me though, I am a flashaholic and that must be taken into account. For my wife, she carries a Peak Brass 5 LED AA light in her purse. The brass is very classy, it always works and she gets 6 months of runtime on a lithium AA cell. The guys at work use either a Peak Matterhorn AAA with 3 Snow29 LEDs or Matterhorn with one red LED.
For me, EDC generally means the light that is always with you. Work EDC is something different and it depends on what you do with it.
When Peak makes a two-stage high/low switch for the Pacific AAA... that will be the EDC for "normal" people I would recommend. It will run a few hours at max brightness on a single alkaline AAA, has a 50% drop off in level for battery saver mode (also tells you to get another battery!) and will decline in brightness for the next 12 hours until there is enough light to get around slowly for another 10 hours. Sounds perfect for people that just keep going and don't pay attention to when they changed the cell in their lights. Yes, it does have a rather large head but the extra reflector size/efficiency makes up for it.
Once I quite bouncing around the world, I would say a multiple output Pacific AAA (running lithium AAA) on the keychain and the FF-III in a tiny belt holster would be perfect for my needs.