I have used both R and MATLAB to solve problems and construct models related to Environmental Engineering and there is a lot of overlap between the two systems. In my opinion, the advantages of MATLAB lie in specialized domain-specific applications. Some examples are:
Functions such as streamline that aid in fluid dynamics investigations.
Toolboxes such as the image processing toolset. I have not found a R package that provides an equivalent implementation of tools like the watershed algorithm.
In my opinion MATLAB provides far better interactive graphics capabilities. However, I think R produces better static print-quality graphics, depending on the application. MATLAB's symbolic math toolbox is also better integrated and more capable than R equivalents such as Ryacas or rSymPy. The existence of the MATLAB compiler also allows systems based on MATLAB code to be deployed independently of the MATLAB environment-- although it's availability will depend on how much money you have to throw around.
Another thing I should note is that the MATLAB debugger is one of the best I have worked with.
The principle advantage I see with R is the openness of the system and the ease with which it can be extended. This has resulted in an incredible diversity of packages on CRAN. I know Mathworks also maintains a repository of user-contributed toolboxes and I can't make a fair comparison as I have not used it that much.
The openness of R also extends to linking in compiled code. A while back I had a model written in Fortran and I was trying to decide between using R or MATLAB as a front-end to help prepare input and process results. I spent an hour reading about the MEX interface to compiled code. When I found that I would have to write and maintain a separate Fortran routine that did some intricate pointer juggling in order to manage the interface, I shelved MATLAB.
The R interface consists of calling .Fortran( [subroutine name], [argument list]) and is simply quicker and cleaner.
