To me the biggest win in Rust is just that, the memory related bugs are nearly non-existent. Throw in a group of people working on something and this makes the project move just so much faster in both review time and time hunting bugs.
IMHO the real big win w/ Rust is not so just memory safety from (some) leaks or segfaults but the fact that the borrow checker rules apply also to concurrency related scenarios and so race conditions and deadlocks become much more difficult to accidentally produce.
Developers can generally be taught to handle memory ownership issues fairly well, esp when helped out with RAII smart pointers, etc.
But in my experience when you throw concurrency in, even very high quality engineers tend to stumble and accidentally introduce race conditions.
In this respect Rust has something over the garbage collected languages, too. Because Java, Go, JS, C#, etc will effectively shield you from "use after free" but they will absolutely not stop you from passing an unlocked, etc. reference to another thread and screwing yourself up royally; and Rust will.
