Although I did not make any formal performance comparisons with other programming languages so far, I can at least assure you that Julia feels quite fast on a day-to-day standard usage to me, especially in comparison to R. On the homepage, however, there are some formal benchmarks listed that indicate a really good performance compared to other languages. Of course, these are just some made-up test cases. Objective comparison in real applications, however, is quite hard to achieve, since languages like R make substantial use of C code in almost any computationally intensive package under the hood. For the sake of both efficiency and reliability, however, I think that researchers should generally avoid usage of low-level software languages like C. As most researchers did never get a true and deep training in software development, such low-level languages simply are too error-prone, especially if you refrain from any thought out extensive and well-structured software testing. So, excluding factoring out code parts into C, I am quite confident that Julia truly is faster than R, and at least equally fast as Matlab. Furthermore, Julia allegedly was designed to enable things like parallel computing and big data handling from scratch.

Nothing comes without a price, however, and hence truly leveraging performance capabilities forces you to deal with data types more explicitly. This happens in Julia to a far lower degree than in C, but it still can be un-intuitive and cumbersome at some points, and it especially complicates the learning process in the beginning. But, dealing with types more explicitly also allows some additional benefits like multiple dispatch, where the behavior of a function can be defined across many combinations of argument types.