I have, and use both. On my keys I have a fauxton on every (I carry at least 3 key rings at work - home, car, and work keys + whatever other keys I need - working in secure areas can be a pain.) ring and assorted AAA devices. I tend to reach for the Ultrafire 602C running a 10440, but i have a Fenix E0 (thanks 4sevens) on the ring with the car keys. The Fenix still has the AAA it came with and still works just fine. The work keys have a fauxton, a strange device with a compass, and a laser pointer. I have to do far more PowerPoint than I am happy with, hence the pointer.
In my work bag I have at least an Ultrafire C3 and enough Eneloops to run it for the rest of the decade (actually for the camera that lives there too) and at least one Orb Raw (1 Luxeon 3 and 1 Cree - one will be on my belt, the other one will be in my pockets).
Counting the lights I normally carry at work, I have 3 fauxtons, 2 strange devices which are basically fauxtons but have compasses attached, 1 Fenix E0, 1 Ultrafire 602C, 1 Ultrafire C3, 1 MTE Rebel light (5 mode CR123 battery), an Orb Raw or two, plus whatever else I'm playing with - usually an incan of at least 300 lumens plus whatever's latest in the toy department. In the car there will be at least a headlamp which lives there plus something powerful. Usually at least one primary CR123 light will be there as well - usually a mod that has too ugly a beam to live anywhere else.
Currently the latest toy is a Nuwai device that their website doesn't admit to (ALX 1213N - if you can find one, buy it and throw away the LED that came with it); running on 3 4/5SubC 1300mAh NiCd cells on a Luxeon I. Replacing this with an SSC P4 LED (T bin) gives you 3x the light output for twice the runtime (290 vs. 570mA current draw). Not to mention a far nicer beam. No nasty green beam colour, no rings. Free lunch anyone?
Just modded one of these for a cop friend - he's delighted. No rings, no green beam and enough runtime for a night shift. This matters seriously to him - as well as more light for longer. He actually called me at home to tell me how delighted he was.
I do get some grief for my light collection given that I work in a psychiatric hospital - one of the student nurses just spent a couple of hours with me on my flashaholism. At least it is less harmful than most of the addictions I deal with day-to-day. Given that I've been a flashaholic for longer than said lassie has been alive...
So runtime/output - who knows? I chose output but I live in a city where we have lost power (on both occasions someone doing silly things with a backhoe) twice since 1990 and both power cuts were for less than 30 minutes on Sunday afternoons (Both of them in daylight).
If I lived where I used to where power was less than reliable (30 blackouts in 20 years - total of all of them less than 6 days) I might go for runtime but it isn't an issue here, hence output.
Doing the other job, I look for power within limits - as in what helps my nearly 50 year old eyes focus on tiny text. This needs a lot of light in a small volume. But mostly lights get used on low as high is to bright for use at 6" range with a magnifying glass.
Suppose it depends on what you want to do. I can rely on the local AC power so my requirements may differ from others. Where a friend of mine used to live (about 5 miles from he nearest pylon) till his wife left him for another woman, runtime was king. He had no mains power at all so batteries had to run for as long as possible. There, about 0.1 lumens would be useful - the light pollution here is brighter than that.
So it depends....
But I'll still go for output. Maybe because I used to use ex-submarine cells through an inverter for power - 2V over 1000Ah capacity. Not that these cells were portable - about 4 of them to the ton. RCR123 cells beat that every time.