Julia's sweet spot seems to be anyone who needs to do statistical work who also has an existing C ABI based environment.
The ability to seamlessly plug in Julia to your production system via C code is a boon for those of us who have to use R in an "offline" capacity and then feed data to production systems.
The downside of alot of the Julia posts is that its not R. R, for better and worse, has many years of bug fixing and library design behind it.
I have yet to stump cran (http://cran.r-project.org/) when looking for a library and after 5+ years of using R I still am amazed that I can learn some new ability that ggplot can do.
My advice to people who ask what language to use is always, I think Julia is still a bit too early on to use unless you already know what code you want to write and are using a C based enviroment.
The reason is that most programmers just want to get one task done. They aren't an expert on the mathematical domain they are trying to use, they just want to plug their values into a library and get their results and maybe print them in a nice format. With Julia I still run into issues too often where you have to second guess the langugage or library and if you aren't fully sure that your math is right you tend to assume you are wrong:)
Otherwise use R. It just works and it will make googling for answers much easier.
EDIT replaced jvm with C ABI. Not sure how I made that big of a typo:(.