I use mathematica at home because I have a legal copy of it... at uni, they only have maple. But that aside, I think mathematica is more useful for most of the stuff I do.. except for my last assignment! I had no idea on how to get an add-on (for smith normal form) to work... which meant I had to go back to uni to do that part of the assignment... grr....
whereas maple has it in its set of original functions, hence easier to figure out.