The impression that I at least have got of Julia is that it's designed specifically for technical computing (mathematics, science, etc.) rather than general purpose programming as Rust is. I think that would be likely to influence what people use it for significantly? That could be a pity, because Julia does look like quite an interesting language.
Rust's REPL, rusti, is presently broken, but it will be being fixed up later.
I presume Rust's safety will also go beyond Julia's, with its algebraic data types and lack of such things as null, and its rigidly checked type system.
Julia's type system is very similar to Rust's. Julia has composite types, type unions and parametric dependent types. It is certainly designed with technical computing in mind, but that does not at all limit its ability to do general purpose programming and in fact can help significantly in high load situations. I personally have done more general purpose programming in Julia than I have done technical computing (and in fact, it's focus on technical computing was one of the least important reasons when I decided to become one of the Julia core developers). You have a good point that the ability to do easy technical computing certainly will influence the initial audience, but, I think, as the language matures, this will shift towards a more general audience.
Rust's REPL, rusti, is presently broken, but it will be being fixed up later.
I presume Rust's safety will also go beyond Julia's, with its algebraic data types and lack of such things as null, and its rigidly checked type system.