Neurons are pattern detectors that can learn to fire for specific sequences of activity over specific sites across their dendrites (the little branches that receive inputs). A neuron has the capability of discriminating hundreds of these sequences. So I guess thats its computing power.
Are neurons like brains? You could make an argument that they are like your neocortex in the sense that brains are networks of areas which interact and different patterns of activity and interaction correspond to different perceptual or cognitive states. Neurons could be seen as similar; they are networks of synapses + dendrites and different patterns of depolarization on the membrane are produced by different sequences of input.>>10801347
An interesting thing some neurophysiologists discovered is that if you have a live neuron population and then disconnect all the connections to one neuron, that neuron doesnt stop firing but continues to do so based on its own intrinsic rhythm.