A related but distinct question might be: How does Rust filesize scale? Meaning, a Hello World application is X, and X is bigger than C/C++. But does Rust outgrow projects in C/C++ as the complexity increases? Or is the code generation actually consistent and all of this is simply about the corelib size and nothing more.
Given that Rust monomorphizes generic functions like C++, and given that Rust uses a high-quality C++ backend for code generation, I'd assume that default binary sizes would be comparable. Producing a more scientific comparison would require implementing a large project more-or-less identically in both languages, which is unlikely in the near future (it might be instructive to compare Servo to Gecko, but Servo isn't near complete yet, and even then Servo does many things differently that might influence the comparison).