I don't think that it is easy to say that model A is better than model B. The fact is that in some applications neural networks fits better than another model such as linear regression. And it usually occurs when there are nonlinearities involved. Though, it is important to evaluate before other aspects. For example: a linear reg model will have less parameters to estimate than a NN for a same set of input variables. Then, a NN will require a larger dataset for its optimization in order to get its benefit of generalization and nonlinear mapping. So, if we do not have enough data, despite of existing nonlinearities involved, a LINEAR reg model may be better adjusted.
Regression is method dealing with linear dependencies, neural networks can deal with nonlinearities. So if your data will have some nonlinear dependencies, neural networks should perform better than regression.
I don't think that it is easy to say that model A is better than model B. The fact is that in some applications neural networks fits better than another model such as linear regression. And it usually occurs when there are nonlinearities involved. Though, it is important to evaluate before other aspects. For example: a linear reg model will have less parameters to estimate than a NN for a same set of input variables. Then, a NN will require a larger dataset for its optimization in order to get its benefit of generalization and nonlinear mapping. So, if we do not have enough data, despite of existing nonlinearities involved, a LINEAR reg model may be better adjusted.
Neural network has a better mechanism to fit and sift through patterns in the historical data, but it is the prediction power you will have to rely on to avoid possible overfitting. This can only be judged based on statistics/metrics of model comparison for a given setting.
It depends to your available data and its validity. Keep in mind that application of neural network needs some data for learning of system and with respect to what you put inside Neural Network for learning you will receive results. I mean appropriate learning data can lead better results while bad data (out layers; and non-treatable data) can make you far away from realistic results. I think combination of statistical approaches and Neural Network maybe useful; but application of statistical approaches for a lot of historical data (for example more than 100 sets) is not very user friendly while for learning phases of Neural Network maybe you need 50-100 sets of data (lower and higher margins). If you have data bank less than 100; application of DX7.0 for statistical approaches can be applicable. I have some published papers in this respect using statistical approaches.