You can compare the ARIMA and ANN models by automatic criteria like the AIC, BIC, SIC, HQ, etc. The model with the lesser criterion is the more adequate and therefore has the better forecasting ability. The issue may not be the software to use.
ANN allows you to identify the most important variables based on the quantity of relative or normalized importance. It will not perform actual predictions, especially the future predictions. I recommend that you use temporal causal modeling approach in SPSS to build your model and perform the future predictions. You can compare the model fitting and accuracy of the ARIMA and temporal causal models using pseudo R squared value and the mean absolute percent error (MAPE).