Great question. Moore’s law cannot be applied to battery technology due to space issues. Computer processors and chip performance doubles roughly every 2 years, and this can be achieved as they use electrons to store information. Electrons are sub atomic particles that surround a nucleus of protons and neutrons. They are so small, that they don’t use space within a computer chip and manufacturing techniques can make chips smaller and smaller without issues.
Batteries work with power as opposed to information, and use ions to transfer charge. Ions are atoms with a charge associated (+ve or –ve) and do take up room, alongside the electrolyte material sandwiched in between the anode and cathode. So generally speaking, a battery 5 times smaller will supply around a 5th of the energy.
As for price, Lithium batteries are more expensive than alternative battery technology, but perform better so are preferable.