And if you compare basic runtime performance of the generated code they come out the same. And this should not be surprising. Most of Rust's safety / lifetime checking is compile-time and incurs no runtime cost. It spits out bitcode which is optimised and turned into machine code through the LLVM backend. The performance of compiling Clang code vs Rust should therefore be quite similar.
And as I said, speed is not the only consideration. Rust may happen to be as fast as C or C++ but that alone would probably mean nothing. I expect the main attraction people see in the language is because it reduces the potential for runtime errors and therefore more stable software particularly in systems programming.