The numeric capabilities of Mathematica are far, far closer to Matlab's than the symbolic capabilities of Matlab are to Mathematica's.

Matlab's symbolic toolbox is actually a wrapper around another proprietary CAS, Mupad.

If I recall correctly, the symbolic toolbox data structures were not first-class citizens in the MATLAB world (where the fundamental data structure was the matrix).

I used the Symbolic Toolbox in grad school to try to simplify equation systems, but once I got the result, I had to rewrite it in real MATLAB code.