I understand that both mean "to be saved/receive help" but that they have slightly different connotations. I can't find any explanation of the difference, however, nor any pairs of example sentences to illustrate this difference.
By using てもらう, it is conveyed that the other is doing something helpful or useful for the action recipient's sake, whereas using the passive られる there is no such nuance and it is more neutral. In the following example, though both sentences are grammatical, the first seems more acceptable to me because this feeling of helpfulness or usefulness is congruent with the context:
〇 お巡りさんに住所を教えてもらった。The policeman told me the address (helping me, indeed).
△ お巡りさんに住所を教えられた。The policeman told me the address. (A more literal translation, in passive voice: I was told the address by the policeman).
In fact, in some cases the passive voice is used when something harmful or negative for the recipient of the action is done, and therefore もらう can't be used in such cases:
地下鉄で誰かに足を踏んでもらった。Someone stepped on my foot in the subway (helping me). This is not correct, because it is naturally a bad or negative action to you, unless you are some foot fetishist that loves being stepped on and are grateful than someone just did it.
〇 地下鉄で誰かに足を踏まれた。Someone stepped on my foot in the subway (bothering me).
助けられる / 助けてもらう
With the verb 助ける, it is already clear that the action is helpful for the recipient, so I agree that the difference between both words is more subtle.