Linux

Unless you're talking about some sort of reference counting, which has to be explicitly added by the programmer in cases where doing so is required for memory safety, I'm not sure what runtime checks you're referring to?

From what I've seen, the performance of programs written in C and Rust are generally the same, more or less, with C or Rust coming out on top with roughly coinflip odds in a handful of cases. This feels like the primary differentiator in performance really comes down to the implementation of the person writing it, and less to do with any performance differences inherent to either language.