Also, microbenchmarks are usually not very good at representing the real world characteristics. But then again, please look at the current version of the linked benchmark.[3] Rust now positions itself in the second place, thanks to the recent improvements given to the Rust programs used in the benchmarks. I believe Rust isn't as fast as highly optimized C, but I think it is safe to say that Rust is just as fast as C++, and both Rust and C++ are much faster than GC'ed languages such as Java, Haskell, and Go.
Edit: I would even say that if Rust's performance is comparable to GC'ed languages, there's no point in using Rust in the first place. Rust is paying a lot of complexity to achieve memory safety without relying on garbage collection.
[1] https://news.ycombinator.com/item?id=9531822
[2] https://www.reddit.com/r/cpp/comments/35pn6h/criticizing_the...
[3] http://benchmarksgame.alioth.debian.org/u64q/which-programs-...