First, electricity is the flow of electric charges. That is, by definition it is not a stored form of energy but a flux. What you store is always internal energy: energy in the nucleus, electronic energy, bond energy within molecules (a multi-electron form of electronic energy), and inter-molecular energy (again essentially electronic energy),or bulk external energy such as gravitational potential energy, electrical potential energy, or kinetic energy
That brings us to the next issue: how do we convert electrical charges to internal/external energy of something and more specifically what kind of internal/external energy
1) Capacitors: Storage as actual separated electrical charges.
2) Pumped hydro storage, ball on the top of a hill: storage as gravitational potential energy
3) A spinning flywheel : macroscopic kinetic energy
1) A phase-change storage: Convert water to steam or ice, i.e., store energy as intermolecular energy), adsorb hydrogen on a storage medium, etc.
2) A chemical/electrochemical battery: Bond energy between atoms in a molecule (intramolecular) e.g., storage by converting water it back to a hydrocarbon fuel. Electrochemical, reducing ions back to non-charge molecules.
3 Create a nuclear fuel maybe.
So where is the difficulty?
1) Depending on which form you choose you are always making two transitions (Electricity--to another form---back to electricity) that are lossy: Say you want to convert electricity into chemical fuel by converting water and CO2 into methane and burn methane to get back electricity when you want. In going to methane you conserve energy but degrade its work potential (the useful part of the energy or exergy). This happens because you generate entropy. I can explain this in detail but this is not the main focus of this question. Essentially there is a thermodynamic loss of useful fraction of energy such that in going from electricity to methane and back to electricity again, you get a smaller fraction back.
2) The storage could be leaky or degrading: Say you were to store as internal energy in a battery. You are adding electrons to this electrochemical system and changing its composition. Every time you go back and forth a few active molecules remain in their more stable state such that after several cycles there are not enough left to store much. Essentially the reason is the same as before entropy generation.
3) There could be a limitation to the capacity of storage: Say you were storing energy by pushing balls uphill or storing water in a tank, there are only so many balls you can take after which your hill has no space left. Similarly if too many charges are pushed on a capacitor there could be dielectric breakdown of the capacitor. If you spin a flywheel too fast (to store more energy) you could shatter it because of rotational stresses.
Each of these three problems exist in each of the energy storage methods.