What's the difference between a rule based system and an artificial neural network?
The difference is vast, although as Dave wrote, the resulting black box might look the same from outside. Rule-based systems are examples of "old style" AI, which uses rules prepared by humans. Neural networks are examples of "new style" AI, whose mechanism is "learned" by the computer using sophisticated algorithms, and as a result, we humans don't really understand why it works. While in some cases rule-based systems could be effective, the general trend in AI has been to switch to machine-learning algorithms such as neural networks, due to their much better performance.