I noticed that the specific heat capacity of brick is around $(900-1000)~\rm\frac{J}{kg~K}$ whereas water is $4180~\rm\frac{J}{kg~K}$.
If my understanding is correct then the water heater would store more heat at the same temperature compared to the brick heater. In fact around 4 times more.
So why are brick filled storage heaters used instead of water filled ones?
Brick is denser than water which means the heater would be heavier which would be another reason to choose the water over the brick.
Though a water heater may be prone to leakage and possible breakage due to thermal expansion, which would be at least one disadvantage of the water heater.