it's been some time since I last looked into this topic, my understanding is that linear regression is not a black box as there exist methods that elucidate how the variables impact the response. On the other hand, neural networks are opaque. Again, been a while so there may be ways to ascertain which inputs were used to generate the weights that led to the response. However, I am skeptical that these methods have the same level of mathematical rigor as those used in linear regression.