Someone on /r/flashlight asked about the differences in specified output and runtime for their new Ultratac K8. I found some of the other answers lacking, so I wrote a really long one that probably no one will even bother not reading since it was posted in a 12h old, low-attention post. So, I’m posting it here, so a larger group of people have the opportunity to decide not to read it 
An AAA NiMH and a 10440 LiIon battery hold essentially equivalent amounts of energy, which is measured in terms of Watt Hours, or Wh (V*Ah=Wh).
Differences in brightness and runtime then are the result of different rates of energy delivery, or power (Watts). These differences end up being, largely, down to the engineering tradeoffs required to hit a specific market niche. In this case, I’d describe that niche as: mid-market brand compact, multi-chemistry, high output.
Let’s consider the factors at play.
As it happens, AAA NiMH (1.2v) and 10440 LiIon cells (3.7v) both carry similar amounts of energy, and can delivery it at similar rates (at least in the 3-5w range we are looking at). In theory then, they should both be capable of both similar brightness and similar runtimes. But, as we know, they aren’t, at least not in the context of this (and other) flashlights.
To understand why, we need to dig deeper, and look at the way the energy source interacts with other parts of the flashlight.
After looking at the input, the energy source, it makes sense to next look at the output, the LED emitter. What we call white LEDs are actually blue LEDs with a layer of florescent phosphor material laid over it. The blue light from the LED excites the various components of the phosphor, which then emit other, generally longer, wavelengths of light, which mix with unabsorbed blue light to produce white. In basic principle, this is how florescent lights work, too, only they are driven by ultraviolet light emitted from excited mercury vapor.
This is perhaps more detail than necessary, but the upshot is, white LEDs start by producing a lot of blue light. Blue light has a shorter wavelength and blue photons carry more energy, and require more energy to produce, which requires relatively high voltages compared to, say Red LEDs, or low voltage transistors, etc. White LEDs then require ~3v.
The 3v voltage of white LEDs meshes well with the 3.7v nominal voltage of LiIon cells, including 10440s. This means that LiIon cells have the advantage of allowing white LEDs to be driven with a basic and inexpensive PWM driver. This means relatively simple and inexpensive AAA lights can achieve high peak output, but at the cost of both efficiency and runtime.
LiIon cell voltage also allows the use of inexpensive regulated, linear drivers, which can be used to trade peak output for constant output and longer runtimes. And, LiIon cells can also be used to power a white LED via buck converters, which can provide regulated output and increased efficiency over 50% or more of runtime. However, with a single LiIon cell, their advantages are generally not enough to justify the added cost/complexity vs a linear or PWM driver.
Meanwhile, single or double AAA cells require the use of a boost driver to drive a white LED. Boost drivers generally offer regulated output. They are somewhat more expensive and complicated than a PWM or linear driver, but the components (small inductors, boost controllers) are produced in huge volumes for various purposes (pretty much any electronics that run off one or two alkaline batteries).
In order to support multiple chemistries, designers have to use a boost converter in order to handle the alkaline and NiMH chemistries. With that requirement set, they are left with the choice of how to drive the LED when powered by a LiIon cell.
Boost and buck converters are both examples of switched-mode power supplies. As such, they share many of the same components and there are designs where those components can be connected in such a way that they allow the same circuit to be used for both buck and boost. It would seem a simple choice then, to use such an arrangement to drive LEDs from either 1.2-1.5v cells, and from ~3.7v cells. And yet, such flashlights seem pretty rare, and tend to command a premium.
I don’t know why buck/boost drivers aren’t more common, but my guess is that their cost is higher because the controller ICs and designs have a much smaller overall market than those for boost converters that allow electronics to be powered only by 1 or 2 alkaline or NiMH batteries.
The next option is a linear driver. One should be able to design and implement a circuit that can be operated as both a boost driver, and as a linear driver. But, once again, these seem rare or non-existent. My guess is that this is, again, a rather small niche, perhaps small enough to require a bespoke design. It is also possible to add dedicated circuitry for a linear driver. This should be relatively simple and inexpensive, in terms of additional components. PCB space, on the other hand, is at a premium in flashlight drivers.
That leaves the final option, PWM, which seems to win out, despite its disadvantages.
This still doesn’t really explain why AAA and LiIon batteries have such different outputs and runtimes, despite having similar energy capacities and power delivery rates; it won’t, until we put all these pieces together.
Lets start by going back to the batteries, because there are some important hidden assumptions there. The AAA batteries could be either alkaline, or NiMH. We’ve mostly been focused on NiMH cells, and its NiMH cells that are neck and neck with LiIon for power delivery rates. But the manufacturers, they often don’t say, but it makes sense that they are referring to alkaline cells, because they the most common, most available, and also because they are less capable than the others, and so their runtimes and output levels define the lower end of the flashlights performance.
Performance with NiMH batteries often ends up being secondary, an afterthought. This can be seen in tests of multi-chemistry lights. Few, if any, have parity between NiMH and LiIon, but for some, NiMH offers a significant advantage over alkalines, while for others, the improvements are marginal. This is, I think, the result of designing the boost section first and foremost around the capabilities of alkaline batteries.
tl;dr
LiIon and NiMH 10440/AAA cells have similar energy capacities and can deliver power at similar rates. Alkaline batteries suck. LiIon cells can power ~3v LEDs at high power levels with very simple driver circuitry, resulting in higher outputs and shorter runtimes.
Multi-chemistry lights need to use boost converters to drive 3v LEDs from 1.5/1.2v Alkaline or NiMH batteries. Flashlight designers spec those boost converters around capabilities of the more common Alkaline chemistry.
NiMH cells power the LED through the same boost circuitry as Alkaline cells. Because they are less common, they are often not a major consideration in design of the boost circuitry. As a result, their output is often constrained below what they are capable of.
I had to write the long version before I could write the short version.
