I would like to respond to a modified version of this question: "How can I make sure the behaviour and numerical results of MATLAB applications are identical across platforms?"
Note that I write "platform" and not "OS", as one important factor in the area of numerical results is the 32bit/64 bit architecture differences and the 32/64 bit MATLAB versions. You may also have slightly different results as of BLAS differences. When using e.g. optimization routines, this can result in large differences. The robustness is depending on data and algorithms.
As for OS, the biggest difference I am aware of is about interfaces with other applications or OS. Like reading from Excel or creating MEX files (being depending on different C Compilers).