It'll depend on your usecase. Prophet is easier to use because FB wrapped everything in a really simple API. ARIMA is still really good if you have someone who is an expert in it. It has been producing useful results for the past like...30 years? If you have someone who understand the concept and can tune it, I'd say go for it. On the other hand, I find that it is extremely hard to explain ARIMA model to business folks. Since ARIMA is basically AR terms and MA terms, which translates into using historical value, and historical error, to predict future values, it makes it really hard to say 'when did something changed?' or 'what is our seasonality?' or 'what is the month to month seasonality for this particular product?' Prophet, on the other hand, gives you really nice components, such as seasonality, trend, holidays, and can be made to easily incorporate other factors, something ARIMA type models can as well...but it is really advance stuff.

Overall...If you're just learning time-series analysis, ARIMA is an important lesson to learn, but for actually doing the analysis/forecast, I'd say use Prophet. Just don't fall into the trap of using a package someone else created without understanding what's going on underneath

In practice I find prophet far superior. Prophet can deal deftly with the kind of problems that show up in real-world data like missing values and radical changes in trend from shocks to the system you're modeling.

For textbook problems like forecasting electricity demand, sARIMA works just fine, but you'll struggle forecasting anything more complex. This is not to say that it's impossible, but it will require far more expertise.

Does anyone have thoughts of using Prophet vs XGBoost time-series analysis?