In short, the maximum possible speed is the same (+/- some nitpicks), but there can be significant differences in typical code, and it's hard to define what's a realistic typical example.

The big one is multi-threading. In Rust, whether you use threads or not, all globals must be thread-safe, and the borrow checker requires memory access to be shared XOR mutable. When writing single-threaded code takes 90% of effort of writing multi-threaded one, Rust programmers may as well sprinkle threads all over the place regardless whether that's a 16x improvement or 1.5x improvement. In C, the cost/benefit analysis is different. Even just spawning a thread is going to make somebody complain that they can't build the code on their platform due to C11/pthread/openmp. Risk of having to debug heisenbugs means that code typically won't be made multi-threaded unless really necessary, and even then preferably kept to simple cases or very coarse-grained splits.