These days, if you go looking for batteries you're likely to find a range of products with some fairly bold claims on their packaging. Standard AA alkaline batteries are the least expensive and have been around for decades, but now there's a bunch of other choices for single use batteries that are marketed as better choices for "digital" devices than the "copper top" or store branded staples we've used for years. Among the newest of these is Energizer's Advanced Lithium and Ultimate Lithium single use batteries.
The the first question that comes to mind is, how much power do these bad boys actually have? Rechargeable batteries are clearly labeled, in fact, we have a couple of AA NiMH ones lying around here that state that they hold 2500mAh of power. With NiMH batteries the formulation can be tweaked to extend shelf life at the expense of total capacity, and we've seen modern batteries ranging from 2100mAh to 2900mAh based upon this. This makes it easy to decide which to get, just do the math and pick your poison.
With single use batteries, it's not so easy. There's no power rating anywhere on the packaging for most alkaline batteries nor is there any on Energizer's Lithium batteries, and in fact the packaging just says 4x for the Advanced Lithium and a whopping 8x for the Ultimate Lithium. But 4 or 8 times what?
The answer turns out to be simple, albeit irritatingly deceptive. All of the current formulations of single use batteries currently sold have a capacity of approximately 3000mAh and a voltage close to 1.5V! We know that this seems like it can't possibly be right. Energizer is claiming 4x and 8x the power of "regular" batteries, and charging a small fortune per 4 pack for these Lithium varieties primarily based upon these claims. So what's going on here?
Apparently, the issue at work isn't how much power each of these battery holds, but how much you can get out of the battery, before it refuses to yield any more of it's energy. Traditional alkaline batteries generate power from a reaction between a zinc electrode that is stuck into a canister containing a paste of manganese oxide. This works well if the power is drawn slowly from the battery, since the reaction can spread throughout the entire volume of manganese oxide in the battery cylinder. Unfortunately this doesn't hold true when power is extracted quickly (as in the case of a digital camera, or other high power devices). When power is drawn out quickly from one of these batteries, the reaction doesn't reach the entire volume of the battery, and the paste that surrounds the zinc electrode ends up coating it with depleted reactants, which cuts the zinc electrode off from the remainder of the manganese oxide it could react with. So while you could get the full 3000mAh out with a low draw device, you may only be able to get 700 or 1000mAh when you're drawing high current with your camera.
Single use lithium batteries are constructed differently. The reactants are placed on a flat sheet, and then rolled up to fit inside the canister of a AA battery. This means that there's a LOT more reaction area, and hence more opportunity to draw as much power as possible out of the battery before a coating can build up on the electrodes. Energizer says that their 4x and 8x claims are based upon this. They also explained that the difference between their 4x and 8x products is the internal surface area. The battery layers are thinner in the 8x device, so have significantly more surface area rolled up into the canister. The Advanced Lithium devices cost less to manufacture than the Ultimate Lithium ones, so there's a nice correlation between performance and price. At least from the perspective of a manufacturer.
So 4x and 8x are actually marketing breakthroughs and not technical ones. And while it's possible to believe that the claims are true and that you can get 8 times the power out of an Ultimate Lithium battery than a normal battery, you really have to turn your thinking upside down to do so. There isn't any way to measure consistently how much you'll be getting out of a traditional battery without testing it in a particular device, and without doing so, any specific claims of better performance lie somewhere between wishful thinking and unconfirmable conjecture.
It's not that these premium lithium batteries aren't better, it's just that there isn't a way to tell if they're 4 or 8 times better, or if they're worth the price premium that they demand.