I'm doing a thesis on tree based algorithm and it works great for medical data.
Granted I have little exposer to NN, you can't do that with NN when clinical trials data is small as hell.
It's all base on the type data and your resource and criteria.
NN is really hype and people tend to over look other algorithms but NN is not a silver bullet. I don't get how you rank those importance either, it could be bias.