I think the main difference between the two is, as someone reading and debugging the code, will probably eventually check even those methods that I assume I know roughly what they do. In contrast, I may not even think to check an overloaded operator unless I _already know_ that it's overloaded.

Maybe a good analogous method would be an overloaded `.ToString()` in C# that has side effects or returns the full text of the Magna Carta or something.