I thought LuaJIT and other Lua runtimes are great for scripting and embedded environments, while Julia focused primarily on being a MATLAB replacement (i.e. desktop environments).

EDIT: Based on comments in the thread, seems both could do the same job but Torch7 has libraries that make running on GPUs easier vs. Julia.

Julia doesn't yet have strong support for running stuff on GPUs.

Support is, indeed, nascent; but it is coming along well:

https://github.com/JuliaGPU

Torch/LuaJIT does?

LuaJIT certainly doesn't at this point; not sure whether torch uses some libraries that do...