As long as you can get the Rust code to compile it's about the same speed. The issue is that rustc is only available on limited platforms (and indeed lack of rustc has killed off entire hardware architectures in popular distros in a bit of tail wagging the dog), rustc changes in breaking ways (adding new features) every 3 months, current rust culture is all bleeding edge types so any rust code you encounter in the wild will require curl rust.up | sh rather than being able to use the 1 year old rust toolchain from your repos.
What good is speed if you cannot compile? c has both. Maybe in another decade rust will have settled down but now wrangling all the incompatible rust versions makes c the far better option. And no, setting cargo versions doesn't fix this. It's not something you'd run into writing rust code within a company but it's definitely something you run into trying to compile other people's rust code.