So, very roughly: the energy density of a battery (what most people are interested in when talking about batteries for practical applications like phones and vehicles) depends on: - The (practically) attainable ionization state of the electron donor (e.g. Lithium [Li+]) and its mass (i.e. electrons per kg) - The electron mobility (how easy is it to make it so electrons flow freely through the electrodes) - The electron acceptor ion density - The redox potential between the electrodes (or: the redox potential of the reaction).
Lithium ion batteries rely on Li, atomic weight 6.94, +1 oxidation state, -3.0401V redox potential. This means that 6.94g of lithium will give you 105 (roughly avogadro's number divided by the number of electrons in a coulomb) Coulombs of charge at 3V = 3 x 105 J per 6.94g or 432 x 105 J/kg which is about 12kWh/kg. Note that this is in stark contrast to practically attainable energy densities (about 250Wh/kg) - of course, the other electrode will weigh a whole bunch, as does the electrolyte and supporting material.
Sodium has an atomic weight of 23 and, as it's in the same group as lithium, can only donate a single electron. Right there, it's already not better than lithium. So what does make it better?
Well, as you can see the contrast between theoretical maximum energy density of lithium vs the actual density we're getting is due to (mostly) the compatible 'other' electrode. Cobalt and carbon are often used in this regard, which are very heavy elements as compared to the amount of electrons they can accept. Sodium has the opportunity to be used with e.g. oxygen, which has a very good electron-to-mass ratio. As Na is also much easier to produce (i.e. it doesn't have to be mined and purified from ore, it's available in wide abundance as a salt already), this may yield vastly cheaper batteries with similar energy densities.
To get to batteries with better energy density, we need to look at heavier elements that can donate more electrons. One of the options is beryllium (atomic weight 9, +2 oxidation state), which also plays well with oxygen. Beryllium is compatible with similar cathode materials as lithium, and allows for practical storage densities in excess of 500Wh/kg.