As of now i think we need to save money in terms because this will give us a good profit in the future while saving in fiat no risk but you can not earn profit on it.
Profit? So all in all you will just saved money because of that kind of purpose.
Fiat in the first place, why it must be saved is to cover your urgent needs and purposes. Why care for profit if we will have to save fiat. Fiat is mostly used as currencies that's why price volatility here is not that active. What does this mean? It will not overvalued even you save it for decades and centuries. It will just changed it's appearance.