People who do Bayes network say it's best, could not have any advice
on NN
I doubt any statement regarding the performance of the model can be reliable as long as they have not been tested against the data.
In your case, I would consider two factors to make my choice.
Feasibility
10k examples with around 20-30 features
It is not a big amount of data. On a very large scale, neural network still have a good (low) training time. Here, you should be able to run both models.
Interpretable model
Bayes network will provide you nice visualization of your data (see per example Bayes Network/Conditional Probability Visualization Tools). It will be harder with neural networks.