Huh? This has definitely not been my experience -- most of the things I've ported over seem to run about twice as fast in Julia as in the original vectorized Matlab (and probably more like 10x faster than naive non-vectorized Matlab)..
With that being said, there are a lot of Julia posts on the subreddit or stack overflow that go like "Why is this Julia code 10x slower than my Python code"? One issue is that getting good performance out of Julia isn't always obvious without a pretty good understanding of how it works. Thankfully, people are willing to help you tweak your code to make it much faster.
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...
https://github.com/JuliaLang/julia/issues/4373
Starting all of Matlab never took that long.