Comparative study between Deep neural nets and Bayesian Networks
They're not directly comparable.  They do different things.  They solve different problems.

A Bayesian network is a probabilistic model of the relationship between multiple random variables.  It is a generative model.  It builds a model of the joint probability distribution between multiple random variables.  It typically requires some priors or assumptions about the structure of the joint distribution.  While it could be used for classification, it normally isn't.

Deep learning is typically used for classification: supervised learning.  It is a discriminative model.  It does not try to model/estimate the joint probability distribution between multiple random variables.  It typically does not require you to specify priors or assumptions about the structure of the joint distribution.