(Disclaimer: I work on Rust and don't have a lot of experience with Nimrod other than reading the docs.)
Nimrod and Rust are in a similar space, yes; they're both systems languages that use compiler backends designed for C (in Nimrod's case, by compiling to C; in Rust's case, through LLVM). I especially like Nimrod's nice Python-like syntax.
Regarding "optional garbage collector", Nimrod and Rust are pretty different: last I looked, Nimrod follows the D route of tying safety to the GC, so if you don't use the GC you also lose memory safety. As far as I know, Rust is still unique among industry languages in that it takes the have-your-cake-and-eat-it-too approach of memory safety even if the GC is not used, via unique pointers and lifetimes.