Rust and Felix both try to be general languages so they're both targeting that. Felix has a better type system. Rust provides more secure but restricted protocol for concurrency, Felix has no such restrictions, it's specifically designed to support shared memory concurrency, which Rust specifically doesn't allow. Rust uses message passing but organises via the memory management mechanism to do it very fast.

I have to delegate that to John (Felix's author) not much of a language theorist myself. It seems to me that Rust wants to be the better/safer C replacement. I think Felix's sweet spot is at a slightly higher level. For example, Felix's garbage collector can indeed be avoided for lower level code, it was meant to be used as an optional feature, but to me it seems it requires more than superficial knowledge to avoid it successfully.