I was wondering about the current state of battery power density, and how batteries compare to things like animal body fat or gravity storage.

Gravity storage is shown in energy per weight-distance using weights 1000x the others, which gives a more realistic scale for which it would be used.

Note that this is just the energy density of the storage technology. To be truly fair, you should probably take into account the weight of the supporting engines etc to extract that energy, and the efficiency of the whole energy cycle. In particular, Hydrogen is very hard to store, and the efficiency of its whole energy cycle is pretty bad. Diesel engines get about 30% efficiency. Li-Ion batteries have 80~90% charge efficiency (power-out/power-in), and Gravity storage claims a 90% round-trip power efficiency.

Li-Ion per Kg is 100x more energy than Gravity per tonne-metre. Also note that concrete is 2.3 t/m^3, and lead is 11.3 t/m^3, so large weights can take up large amounts of volume too. So a 10t lead weight of nearly 1m^3 volume with a 10m drop would give you about the same energy as 1Kg of Li-Ion Battery, and the same weight of fat would give you 40x as much as Li-Ion.

This shows just how amazing Diesel, Fat, and even Carbs are compared to current battery tech. No wonder flies carry enough energy to stay airborne all day.

A Li-Ion Tesla powerwall has 12.5 kWh of capacity, and weighs 114Kg. An equivalent gravity storage unit with a 10m drop would need 500t of weight, or 44m^3 of lead (a 11m*2m*2m block). This is the same as 1Kg or 1.2 litres of Diesel, but a diesel generator is only about 30% efficient and gets about 3kWh/l, so in practice you need 4l of Diesel for 12kWh.

The Li-Ion Telsa big battery in South Australia has 129MWh of storage, and must be at least 10,000 powerwalls, and be at least 1kt of battery.

Large scale gravity storage plans are looking at using at least 100Kt weight with 100m drop which is 27MWh of storage.