Logistic Regression vs Deep Neural Networks

The picture is accurate, but the more relevant question is "When would each technique be at an advantage?" The obvious difference, correctly depicted, is that the Deep Neural Network is estimating many more parameters and even more permutations of parameters than the logistic regression. Therefore the real question is in what situations would that be a good idea? You need a good ratio of data points to parameters to get reliable estimates so the first criteria would be lots of data in order to estimate lots of parameters. If that's not true then you'd be estimating lots of parameters with little data per parameter and get a bunch of spurious results.