This is due to its ability to learn, adapt and to find the most appropriate relation between inputs and output variables. Also, It has the ability to tolerate relatively imprecise task, approximate findings and even has less sensitivity to outliers.
In regression models independent variables should be mutually independent of each other, also, there is a linear relationship between dependent and independent variables and the residuals (the value of errors between the real observed value and the regression value) should have a normal distribution and should be uncorrelated with the independent variables. Artificial Neural Network (ANN) has less strict conditions, it is a model-free technique; this is data-driven technique-ANN does not make rigorous model assumptions like normality, linearity, and independent variables that are mutually independent. This is the reason why ANN is potentially more promising than regression models.
The main restriction of regression models is the linearity they assume, the independence of variable they require and mainly gausian distribution of variables they expect. This limits their success. Some regression models overcome this limitation to a certain extend, e.g. Support Vector Regression. But the recent development in computational power allows very complex ANN that have none of the regression limitations and are even able to incorporate multiple past states of variables at the same time.