What factors determine the energy storage capacity of compressed gases?

[Philip Wood]

So, why carbon nanotube springs have better energy density than steel springs?

The energy stored due to tensile stress per unit volume of solid is $u = \frac{1}{2}Y \epsilon^2$ in which Y is the Young modulus and $\epsilon$ is the strain.

Both factors, Y and maximum possible elastic $\epsilon$ are different for the two materials. The carbon-carbon covalent bonds exert more force per unit increase in separation of the atoms than the metallically bonded atoms in steel, leading to the nanotubes having a greater Young modulus than steel. Also, much larger strains can be suffered by the nanotubes than by steel before the material ceases to deform elastically. This is because the metallic bonding (pooled electrons) in the steel allows planes of atoms in crystals to slip over each other (promoted by the presence of dislocations) under moderate stress. This can't happen in the covalently bonded nanotubes, though they do break eventually under VERY large stress.