Overall I'm excited for Julia, but have a lot to learn. As far as Octave/Scilab type applications go, I find them useful for small systems where I need to make sure the math of what I'm doing is correct before writing it in something like Julia or Python + Numpy. Excel is also surprisingly good for the really simple stuff (Ex: inverting a small matrix and doing some matrix multiplications).
A few years ago I think there were some performance regressions in Julia relative to JIT'd Python (which, using LLVM like Julia, is way faster than normal Python). This seems to be mostly fixed now.
In the example above, the OP was getting 2ms in Numba vs 8ms in Julia three years ago, and recommendations from Julia folks were able to get the latter down to parity with an equivalent algorithm or 386us with an improved algorithm.
On my laptop today, I seem to get 2.0ms in Numba, 2.7ms with Julia 1.0, and 80us using the improved algorithm in Julia 1.0 (and, just to drive home the importance of compilation, 780ms in Python without Numba).
[1] https://old.reddit.com/r/Julia/comments/3x6tg9/why_is_this_l...