I really liked this article by Bryan Cantrill from 2018:
https://bcantrill.dtrace.org/2018/09/28/the-relative-perform...
He straight ported some C code to rust and found the rust code outperformed it by ~30% or something. The culprit ended up being that in C, he was using a hash table library he's been copy pasting between projects for years. In rust, he used BTreeMap from the standard library, which turns out to be much better optimized.
This isn't evidence Rust is faster than C. I mean, you could just backport that btreemap to C and get exactly the same performance in C code. At the limit, I think both languages perform basically the same.
But most people aren't going to do that.
If we're comparing normal rust to normal C - whatever that means - then I think rust takes the win here. Even Bryan Cantrill - one of the best C programmers you're likely to ever run into - isn't using a particularly well optimized hash table implementation in his C code. The quality of the standard tools matters.
When we talk about C, we're really talking about an ecosystem of practice. And in that ecosystem, having a better standard library will make the average program better.