Julia is aiming at Matlab while Clojure is aiming at JVM/Lisp. If you're used to using Matlab for scientific computation then at some point Julia will become a much better option. Much of their work is around lifting heavy numerical components up into the runtime which are wasted on a lot of the programming one would do in something like Clojure.
Julia isn't (currently) targeted as a general-purpose programming language, but there's nothing in the core language that's specialized for scientific computing. While the linear algebra libraries etc. are part of the standard library, they're either written in Julia or wrappers for external projects. Its closest relative in terms of paradigm is might be Dylan (http://en.wikipedia.org/wiki/Dylan_programming_language), which Apple intended as a lispy general-purpose language for the Newton. IMHO, making it useful in the domains where people use Clojure is really just a matter of library support (and whether you can tolerate 1-based indexing).
While that's true, I can't believe that given its numerical bent it'll take anything less than an incredible push to move it to a more general playing field.
I'd say they're pretty different niches.