(I'm personally using NN models for predicting certain values for tabularly structured data and at least for my case, the NN works better than state-of-the art tree models.)
For example, take the circle dataset here: https://playground.tensorflow.org
That doesn't look immediately linearly separable, but since it is 2D we have the insight that parameterizing by radius would do the trick. Now try doing that in 1000 dimensions. Sometimes you can, sometimes you can't or don't want to bother.
The magic of deep neural networks comes from modeling complicated conditional probability distributions, which lets you do generative magic but isn't going to give you significantly better results than ensemble kNN when you're discriminating and the conditional distribution is low variance. Ensemble methods are like a form of regularization and they also act as a weak bootstrap to better model population variance, so it's no surprise that when they're capable of modeling the domain, they perform better than unregularized, un-bootstrapped neural network model. There are still tons of situations where ensemble methods can't model the domain, and if you incorporated regularization and bootstrapping into a discriminative NN model it would probably perform equivalently to the ensemble model.