It is not easy to decide, and based on the data under study some researchers concluded ANN is better than ARIMA and others concluded the opposite. The best way apply both for your data and based on your results you can decide.

to my knowledge those are really different frames since such ANN should behave in a weakly dependent way (close to independence, even wether main differences do hold), and ARIMA are long memory

moreover ARIMA are linear (or of a moving average type wrt innovations, which is definitely not the case for ANN models

A main problem is to understand where are data coming from

From my experience, I suggest that you first see if your time series are linear or not. In the latter case, the suggestion is to use non-linear models, because they are ANN ...;-D

Again, (for understand): From my experience, I suggest that you first see if your time series are linear or not. In the latter case, the suggestion is to use non-linear models, for example ANN

ARIMA is mainly a linear time series model while ANN is one of the many non-linear time series models. In my suggestion, you need to build an adequate linear model (ARIMA) after which you can test for nonlinearity. If it does exist, you can go ahead to entertain a non-linear model (like the ANN).

Traditional ARIMA models are better, from my experience, especially when the data is characterized by high variability. It's general answer.