eagle-
"a few of the cheap 18650 batteries, Rated for 5,000mAh," You'll find some folks on the candlepower forum regularly do tests for capacity. And they regularly get the same results: 3300mA is about the most that anyone can actually get from an 18650 battery. Ask yourself, why is it that the top brand names, the companies that invest billions in engineering research, including Panasonic, can only get ~3300mAh out of these cells? The answer is that there is an energy density limit to the chemistry involved, that's simply as far as they ALL have been able to get.
The masked strangers who claim to get more? Invariably are liars and thieves. And worse, sometimes the corners they cut lead to fires and explosions, because lithium battery chemistry is, like nitroglycerin, something you just can't mess around with.
Go online and look at the Ultrafire web site, in China. Look at their products, according to the maker. Now go look at ebay and Amazon, where you will find "genuine Ultrafire" batteries from a dozen sources. Except, none of them is the same color sleeve that Ultrafire says they use. And all of them have the voltage wrong (i.e. 3.8 instead of 3.6 volts) or the capacity over 4000mA when the real limit is...that same old 3300mA.
Plenty of cheating to go around. And the folks who make them and sell them, know damn well they are thieves.
fm-
"Something like a Sola uses a driver with a voltage booster." Close. But what makes an LED bright is the current applied to it, not so much the voltage. If you make a cheap light where the battery voltage roughly matches the voltage that the LED can run on, that's cheap and it works. If you want a better light, you add a chip that supplies the *correct* amperage, and you ignore the voltage (ignore it, because the choice of battery limits it anyway), and you get predictable steady brightness and LED life. And you get to choose how much current is applied and how bright the LED is.
Then there's a third situation, where you will get the LED growing dimmer as the battery runs down, regardless of how you are trying to control it.
Many ways to skin a cat. As PETA might say, any one of them that involves alive cat is simply wrong, no matter how well it works.