Rice professor James Tour says that graphene memory would increase the amount of storage in a two-dimensional array by about five times. He says that this massive improvement is due to the individual bits being able to be made smaller than 10 nanometers. By comparison, circuitry in your average flash memory chip today is 45nm. Another big benefit of graphene memory is that switches can be controlled by two terminals rather than the three terminals used in flash memory today.
The two-terminal capability is important because it provides the capability to make three-dimensional memory practical since the very thin graphene arrays can be stacked, multiplying the storage capacity of the array with each graphene layer.
Advantages? No moving parts, and a million-to-one improvement in power consumption.