Honestly I'm not sure. Modern GCs are pretty good, and manual memory management isn't a free lunch either. One major advantage of a GC is it can batch all the `free`s together which is a lot more efficient than the manual approach where you free objects individually in a pseudo-random order.
Isn't that what Rust is all about?
Rust is for memory safety. GC software is a way to achieve some form of memory safety while also being much simpler and faster to write compared to Rust.