A broad road = a wide road A broad river = a wide river They seem to be synonymous at least when we are examining two-dimensional physical objects that are simply much greater in one dimension than the other. Otherwise, there is no rule that I can perceive; it is collocational or idiomatic. For what it is worth, Fowler says that ' wide refers to the distance that separates the limits, and broad to the amplitude of what connects them, and when it does not matter which of these is in our minds, either word does equally well'.
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