CR123A, AA, and AAA are just sizes. You can get lithium cells in AA and AAA sizes, and they outperform their NiMH and alkaline in most applications. There's nothing magical about the CR123A size except it provides a good combination of size and energy for a lot of lights.
Using a particular kind of battery doesn't guarantee that a light will be brighter or better than another. It takes a certain amount of power to light the LED and, everything else being equal, more light requires more power. Now, a battery holds a certain and limited amount of energy. The energy is the product of power and time. So for the same energy, you can produce a lot of power (a lot of light) for a short time, or a little power (less light) for a longer time.
For their weight, and to a lesser extent their volume, lithium cells contain more energy than NiMH or alkaline cells. So for the same weight or size, you can have more light or more run time or some of both if you use a lithium cell than if you use NiMH or alkaline. But there are plenty of flashlights which put out a lot of light and/or run for a long time from NiMH or alkaline cells. (Alkalines have other limitations when used in high output lights, though.) It's just that if you filled the same battery compartment with lithium cells, you'd get either more light or longer run time or some of both.
Lithium cells are considerably more expensive than alkaline and NiMH, and the difference is extreme if you have to buy them at a drug store, when traveling for instance. And overall it's much easier to find alkaline AA and AAA cells than any kind of lithium, in roadside mini-marts for example. Those are probably the main reasons lights using alkaline and NiMH cells remain popular.
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