As we mentioned in Chapter 2, Using Deep Learning to Solve Regression Problems, deep neural networks aren't easily interpretable. While deep neural networks are wonderful predictors, it is not easy to understand why they arrived at the prediction they made. It bears repeating that when the task is to understand which features are most correlated with a change in the target, a deep neural network isn't the tool for the job. However, if the goal is raw predictive power, you should consider a deep neural network.
We should also give consideration to complexity. Deep neural networks are complex models with lots of parameters. Finding the best neural network can take time and experimentation. Not all problems warrant that level of complexity.
In real life, I rarely use deep learning as my first solution to a structured data problem. I'll start with the simplest model that might possibly work, and then iterate to deep learning as the problem requires. When the problem domain contains images, audio, or text, I'm more likely to begin with deep learning.