Quote from prophet:
Matlab's average performance was tested to be 5 times better than Mathematical for various numerical operations.
that matches my experience, matlab is noticeably faster for crunching numbers. post wasn't meant as a "mine is bigger than yours" swipe, both are fab tools and either will do more than 99% of us could ever dream up.
mathematica's strength - and this certainly YMMV territory - is that it is much faster in getting from the germination of an idea to full-blown testing of the idea. it's just a terrific development platform. 90% of my time is spent in development, not crunching, so for me this is huge advantage. it is also very very easy to go from testing things out to presentation/documentation, which is a major issue (for me) with Matlab.
some examples of Mathematica based quant offerings...
http://www.ifs.dk/DerivativesExpert/DerivativesExpert.html
http://www.unriskderivatives.com/product/examples.html
a book with lots of goodies..."Modelling Financial Derivatives with Mathematica"...
http://www.ifs.dk/DerivativesExpert/DerivativesExpert.html
again, both platforms are terrific, no complaints about either. there was a time i simulated ridiculously complex systems - we were designing silicon-based retinal workalikes - where Matlabs speed advantage really did matter more than anything else.
if i had to generalize - if all you're doing is grabbing price data and looking for patterns, time series, etc, Matlab is probably a better fit, if you're testing using pricing models, monte carloing, etc, Mathematica will probably be an easier path.
oh...Wolfram has a 64-bit version for 64-bit linux running on Athlon/Opterons. very very nice.
