I have used both in the science context and found Julia much better suited for mathematical problems. Matrix/vector support built into the language is a huge advantage. On top, running code in parallel environments is better supported by Julia (Macros, scheduling, etc...). On top of it, Julia has an excellent Python interface which makes it possible to also use this huge ecosystem of libraries. Makes it easy to use matplotlib out of the box.

I like Julia as well, but there is an interesting scientific library for LuaJIT:

http://torch.ch/

Anyone have experience with it?

having worked with it, torch is amazing for neural network stuff (thanks to the nn rock); however it raises the same problems there are with Python. Lua is basically a wrapper around C/C++ and whenever you need to do complex stuff, you find yourself writing C/C++ rather than Lua.

Isn't LuaJIT development stale?

Yes. Lua could have been the Julia of its time if they had decided to pursue a more advanced compilation system rather than trying to embed lua everywhere in everything. Luajit is fast because of the nature of optimizations upon the tables structure and single table architecture. Julia is a better, faster lua and I don't find myself missing being able to embed my code when I can just call into what I need FROM julia.

I've used both. Lua is powerful because of torch and it's GPU computing capabilities, but in terms of ease of use and modern syntax, Julia is lightyears ahead.