I have been using Mathematica regularly for five years now and I am a new user of Julia. As a first serious project I have used Julia to simulate a nonlinear optical pulse propagation problem. I originally have written the codes in Mathematica. The simulation time in Julia was roughly eight times smaller than Mathematica. I am sure I have missed many Julia tricks to make it even faster. In mathematica Table or ParallelTable are quite fast. I am disappointed that with the new version 10 Wolfram has not added any more parallel computation details. So for symbolic manipulation or doing a quick plots mathematica is unbeatable. Writing some basic parallel codes are also as trivial as it gets.
One feature I would like to see from IJulia may be is that the input of greek and mathematical symbol in way that looks natural, e.g. using subscript, in division, integration etc as way to input. This will definitely be a significant improvement IMHO. second feature is to be able to plot a function in a way one can do in Mathematica. Plotting packages for Julia does this in very limited way (unless I am missing something)
