Weirdly, Mathematica integrated support for high-performance numerical linear algebra libraries from Intel and others a couple years before MATLAB did.

So your point about symbolic versus numeric flavor might have been correct prior to version 6, but it is no longer true (Mathematica 10 will be released later this year). In fact, they now use many of the same libraries for pure numeric work.

Numeric (as well as hybrid numeric+symbolic) computation is possible in Mathematica. In MATLAB, symbolic math requires a clunky add-on that is far from competitive with what Mathematica can do.

I work at Wolfram.