What I like most about SymPy is how straightforwardly it maps onto how you actually do math by hand. The domain objects are things like variables, expressions,

What I like most about SymPy is how straightforwardly it maps onto how you actually do math by hand. The domain objects are things like variables, expressions, equations, and the operations are things like "differentiate", "set equal", "solve for X". It feels like it just automates the stuff I would already do: a bicycle for doing algebra. Most other CASes seem to have a more "magic calculator" interface, where you plop down some crazy integral and it spits out a closed form. This is useful of course, but it has nothing really to do with doing math. I'm sure both styles are possible in either one, that's just the spirit I feel like each one has.