Is there a significant difference between "sobre" and "acerca de", when the intent is to describe the topic of something?
Where is "acerca de" a better choice than "sobre", and vice-versa?
The word "sobre" can become, has the potential, to be a synonym of "acerca de"; when used as a preposition.
Although "sobre" can be used as a synonym; it is context dependent and can have multiple meanings. It is true that "acerca de" is a bit more precise, there is just one way of using it, only one meaning.
Examples of this ambiguity:
synonym of "acerca de"
Those examples are for "sobre" used as a preposition, actually it can be used on three different forms:
That is why it is context dependent.
They are exact synonyms (as RAE says), you can use any of them to replace the other because there's no difference in meaning or grammar.