Why is Bayesian filtering better than Neural Networks when classifying spam?
It would be interesting to know what litterature you have read.

As far as I know, Bayesian filters were working very well. That's because the learning is based on the words used, and a Bayesian filter is quick to understand that an email containt "Viagra" is likely spam.

But spammers are not so stupid, and they quickly introduced mispelled word. "VI4GRA" has never been seen in any spam before. In a word: it's easy to work around a Bayesian filter.

Neural Networks can be good at classifying. But there are two difficulties: the choice of measures ; the training data.