A biological neuron has two kinds of dendrites: distal and proximal. Only proximal dendrites are modeled in the artificial neurons we see today.
Nerve cells in the brain also have what, ~20 different chemical neurotransmitters modulating the state of the neuron in question, and this looks a lot more analog than digital... any kind of one-to-one correspondence between biological brains and digital learning networks never seemed all that realistic to me.