benchmark polynomial systems leads to a few hits, including the University of Mannheim's Computer Algebra Benchmark Initiative. Sadly, most of these are out of date or defunct. The most active seems to be the SymbolicData Wiki, but as far as I can tell, it only collects benchmark problems, not benchmark results.
Some comparisons (dating back to 1996) of Axiom, Macsyma, Maple, Mathematica, MuPAD, and Reduce solving polynomial systems can be found in Hans-Gert Gräbe, About the Polynomial System Solve Facility of Axiom, Macsyma, Maple, Mathematica, MuPAD, and Reduce, Preprint 11/96 des Instituts für Informatik, Universität Leipzig, Germany, December 1996. The conclusion is that Axiom, Maple and Reduce win due to their using Gröbner bases (the others did not at this point in time), with Maple coming out slightly ahead of the others.
There's also an old comparison on the SINGULAR website showing SINGULAR 2.0 (current as of December 2015 is 4.0.2) beating Maple, among others.
On the other hand, a more recent publication (Yao Sun, Dongdai Lin, and Dingkang Wang. 2015. On implementing signature-based Gröbner basis algorithms using linear algebraic routines from M4RI. ACM Commun. Comput. Algebra 49, 2 (August 2015), 63-64 compare the authors' implementation of a Gröbner basis algorithm with that of Maple, Singular and Magma, with Magma being faster than the other two packages by an order of magnitude (and tying with the authors' implementation).
So it seems to depend very much on the problem (size as well as structure) and the software version which package is the fastest. Nevertheless, the recommendation to use an actively developed, special-purpose computer algebra system such as Singular, Magma or Maple rather than a general-purpose symbolic computation software is a sound one. This goes double for a toolbox in a numerical software, which adds another level of overhead and is usually several versions behind the stand-alone software they're based on (MuPAD, previously Maple, in the case of Matlab's toolbox).