According to your experience with time series forecast, in which cases is ARIMA better than a Neural Network, be it a LSTM or a CNN ?
ARIMA is a parametric method and it should work better for relatively short series when the number of observation is not sufficient to apply more flexible methods.
However, the only way to find out which method is better is to perform out-of-sample analysis.
Let me recommend this chapter containing instructions of how to compare alternative forecasting methods:
Chapter Forecast Error Measures: Critical Review and Practical Recommendations
As I experienced, it isn't generally true that ARIMA method is better than ANN.
It depends to your data, sample size, ...
Sometimes ARIMA is better the ANN and sometimes ANN is better. You should fit both of them and compare goodness of fit measures to identify the better model.
Based on the stochastic characteristics of your data, ARIMA, Smoothing methods, or ANN can the best; so you need to evaluate the accuracy of these techniques using the data under study.
This chapter may help you:
https://otexts.com/fpp2/accuracy.html
The rolling origin evaluation scheme as described in https://otexts.com/fpp2/accuracy.html is a good approach, but the MASE measure has some disadvantages as described in this chapter:
Chapter Forecast Error Measures: Critical Review and Practical Recommendations
So I would recommend to use the rolling origin evaluation, but to use the AvgRelMAE instead of the MASE (as described in the above chapter).
It is also important to mention that if you want to use MASE/AvgRelMAE, you need to optimize your forecasts for the symmetric loss function first (this issue is also addressed in the chapter).
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