I'm mostly using the Option-way currently, but as far as I can see, both these ways have drawbacks:
With the Option method I pay a runtime cost every time I want to access a member of that struct during the "regular" time of life of that struct. Also, there are more possible error-paths.
The mem::replace method is in a way just the Option method in disguise: The value that I create to replace the precious value must be created at that spot in the code, which usually means that it is some disfunctional state and kind of a None anyway (think a unopened file). The problem here is that, if it is possible to construct such a null-like value, then the member functions of the struct typically have to deal with that possibility too and check before each access, which is like doing if let Some(x) ....
Ultimately, I want to make useless/disfunctional state irrepresentable, but both the Option as well as the mem::replace method require a useless/disfunctional state to be possible.
With this method I can avoid disfunctional state, and re-use the fields after drop.