Rust is roughly similar to C in most of these benchmarks and beats it in a few: https://benchmarksgame-team.pages.debian.net/benchmarksgame/fastest/rust.html

Arguably when LLVM gets a bit better, Rust can be even faster than C because rust can be optimised in more places safely than C code can. The issue is that LLVM wasn't written with that in mind, so some performance is left on the table.