Well that only depends on what gadgets happen to be available, doesn't it? Both C and JS get compiled down to machine code.
I personally would not trust that you couldn't, in the most extreme case, get close enough to the kernel (like the PoC does through system calls) to mispredict it into leaking any kernel-mapped memory through a timing side channel. And nowadays, kernels typically map almost all physical memory in their shared address space (it's not too expensive in a 64 bit address space).
EDIT: See my extended reasoning here: https://news.ycombinator.com/item?id=43991696