[jacquesm]

It can transmit continuous variable state rather than discrete state in pulses.

Of course you can still transmit continuous variable state indirectly using pulses (for instance, using pulse width modulation or frequency modulation) but it requires a bit more hardware.

Probably there is some kind of cross-over in complexity of the neural structure (density, length of the individual neurons) where it makes more sense to switch to a digital mode (cross talk for instance).