Ok, I got around to doing some measurements. Current clamp, averaged over a couple of seconds.
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The only active electronics in them are the battery protection circuitry which should be minuscule draw. On a standard M12 2.0 battery, the run times should be approximately:
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On a 6.0XC battery, the LED lights would basically last forever.
One other big benefit of the LEDs is they are WAY cooler. I ran the incandescent just long enough for it to warm up and the current to stabilize, and when I went to swap back to the LED bulb I had to wait like 10 minutes for it to be cool enough to grab! Also, the LED version of the light's build quality is impossibly better than the incandescent one. The incandescent frankly feels like creaky plasticky trash, whereas the LED version is much more solid, and the head of it is even cast aluminum!
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You can also see there what I was talking about earlier how the reflector design is very different for an LED.
Here's a closeup of the LED replacement bulb I have vs. the original incandescent:
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The overall conclusion here is, if you already own the incandescent version, the LED bulb is better in some ways, but unless you can get it for cheap you're probably better off just throwing away the old one and buying an LED version since they are on eBay right now for 29$ and are a better overall tool.