An interesting quote.
Replicating functioning of the brain, or some major subsystem of it, is no doubt going to require far more than just billions of parameters. The cortex contains >15 billion neurons, but there are also the neurons contained in all the other brain structures. Furthermore, neurons connect via dense dendritic trees, the human brain having on the order of 100 trillion synapses.
Adding to the complexity, neurons have numerous "communication ports", including numerous pre- and postsynaptic neurotransmitter receptors, and a wide range of receptors for endocrine, immune system and other types of signals. Message propagation typically involves as well the layer of complex intracellular "second-messenger" transformations.
While it's highly probably future NNs will be developed that do even more amazing things than now possible, I think the challenge of equaling what real brains do is to say the least enormously daunting.
Somebody smarter than me could probably figure out the magnitude, how many nodes or weights it takes for a NN to function like the brain, though I imagine it will be a really impressive number.
Edit: typos