The Quantum Battery pack mentioned is not at all like the Yongnuo. The Quantum is expensive because it has it's own battery and voltage regulator. It is not a compartment that holds batteries like the Yongnuo. The Quantum will out perform the standard battery packs like the Yongnuo in number of flashes and recharge time. That is what you are paying for.
This not correct information about the Yongnuo external battery pack. It is NOT merely a AA battery compartment, far from it.
Speedlights do use AA batteries, typically four to output 6 volts. These AA batteries go into a AA battery compartment. The speedlight necessarily also builds in a power converter and voltage regulator to convert 6V to around 325 volts to directly charge the flash capacitor that powers the flash tube. This power converter current is the whine we sometimes hear at recycle.
Some speedlight models have
another high voltage connector where an external battery pack can be plugged in. The battery pack also includes a similar power converter and voltage regulator which outputs
around 325 volts, and this high voltage connector goes directly to the flash capacitor. Now there are two voltage sources, internal and external, two 325 volt sources, charging the flash capacitor, for faster recycle and larger longer battery capacity. The original 6 volt AA cells also powers the rest of the electronics, so the AA batteries have to be there too.
The Yongnuo SF-18 battery pack plugs into the Nikon speedlights using the SAME high voltage connector that the Nikon SD-8 and SD-9 battery packs plug into. Canon is the same deal. That external connector is a 325 volt connector. The external package is NOT merely a battery compartment. If it were merely a battery compartment, it would have to plug into the speedlight battery compartment, which it does not.
I know little about Quantum, but the specs make it obvious that some Quantum batteries are 6V lead acid, but others use a NiMH battery pack. I don't know how the Quantum NiMH batteries connect, but the 6V lead acid has to be connected into the flash AA battery compartment, replacing the original AA batteries, and simply furnishes 6V with a much longer capacity duration (a bigger 6V battery). Lead acid batteries also have a much lower internal impedance, and so recycle (from the flashes own power converter) can be much faster recycle using 6V lead acid instead of 6V of AA alkalines. Rechargeble NiMH batteries are about twice as fast as alkalines, but not as fast as lead acid.
For example, another source of such replacement 6V lead acid battery pack is the Al Jacobs Black Box:
PRODUCTS and SERVICES | www.ALJACOBS.COM which necessarily plugs into the flash AA battery compartment (typically using Quantum cables and connectors, because they are available). Longer life, faster recycle than AA batteries, but is still NOT a high voltage power pack like the Yongnuo SF-18. In this sense, the lead acid batteries are merely another battery compartment.
The Yongnuo SF-18 battery pack uses AA NiMH,
but it definitely outputs 325 volts to charge the speedlight flash capacitor directly.
It will work with alkaline AA batteries too, but alkalines will recycle much slower than NiMH or lead acid (alkaline is high internal impedance).