Its a matter of connotation. Basically they're the same. 'Depend on' would mean there is some condition that is an input that will affect the output. 'Is New York a great place to live? It depends on who you ask. 'Hinge on' is a more specific and less frequently seen phrase. It would refer to a very SPECIFIC input, that will make an outcome be either very positive or very negative, like a door swinging on a hinge. The immigration debate hinges on the election results.' Its a very specific example of 'depends on.' You could almost always substitute depends on for hinges on, but not the other way around.

Hi Nanako, They do mean basically the same thing, but "hinge on" is a much stronger way of saying "depend on". For example, in the sentence you mentioned, "The success of the project hinges on the effectiveness of the ad campaign", the writer is implying that the ad campaign is the most important factor in the success of the project. If he had said "depend on" instead, the implication would be "the ad campaign is absolutely necessary to the success of the project." You could replace "hinge on" with "depend on", "hinge on" is just more emphatic. Hope this helps!