The human brain is one of the great mysteries of our time and scientists have not reached a consensus on exactly how it works. Two theories of the brain exist namely the grandmother cell theory and the distributed representation theory. The first theory asserts that individual neurons have high information capacity and are capable of representing complex concepts such as your grandmother or even Jennifer Aniston. The second theory neurons asserts that neurons are much more simple and representations of complex objects are distributed across many neurons. Artificial neural networks are loosely inspired by the second theory.

One reason why I believe current generation neural networks are not capable of sentience (a different concept to intelligence) is because I believe that biological neurons are much more complex than artificial neurons.

A single neuron in the brain is an incredibly complex machine that even today we don’t understand. A single “neuron” in a neural network is an incredibly simple mathematical function that captures a minuscule fraction of the complexity of a biological neuron. So to say neural networks mimic the brain, that is true at the level of loose inspiration, but really artificial neural networks are nothing like what the biological brain does. - Andrew Ng

Another big difference between the brain and neural networks is size and organization. Human brains contain many more neurons and synapses than neural network and they are self-organizing and adaptive. Neural networks, by comparison, are organized according to an architecture. Neural networks are not "self-organizing" in the same sense as the brain which much more closely resemble a graph than an ordered network.