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In order to understand whether Cadabra is useful for you, a comparison to other system may help. Without going too much into detail, here are some notable differences and similarities with other systems.
Cadabra is predominantly a 'field theory aware notebook'. What this means is that is is designed to be useful for the manipulations of patterns which occur in the description of field theory problems. It knows about patterns more than it knows about the mathematical meaning of those patterns.
Other programs in this class are FORM and its predecessor Schoonship, which both know relatively little about the maths of physics which people do with them, but primarily provide a cleverly thought-out toolbox of algorithms to manipulate expressions. Just like when you compute things with pen and paper, you can do things with these programs which are manifest mathematical nonsense.
Programs like Sage (with SageManifolds) and xAct tend to be much more strict in how you define your problem: they know a lot about the mathematical meaning of symbols, and
Neither of these approaches is best, they are just different.
Cadabra is intentionally not designed to cover 'as much of mathematics as we can implement'. It is specifically meant to help solving a particular class of problems which occur in field theory. This is in part because of its roots (it originally was just a simple tool to help write research papers), and in part because I do not believe that a 'megalomanic' approach can work.
Programs like Mathematica, Maple and Sage have a different philosophy. They try to target, not always with success, a very large audience, by aiming to cover 'all of maths'.
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