Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors.
Most of these features are included in Symbolica in some capacity (ODE solving is missing) and there are CAS features Symbolica has and that Maxima has not (like advanced pattern matching), even though it is only a year old.
It is not just a matter of whether a feature is there, it needs to be usable in practice. You cannot use Maxima to do computation with large rational polynomials as this paper shows:
Symbolica is 10 times faster and uses 60 times less memory than Maxima on a medium-sized problem. The larger sized problem does not run with Maxima. Note that this is tested with an older version of Symbolica, the latest version is even faster.
> Symbolica is 10 times faster and uses 60 times less memory than Maxima on a medium-sized problem. The larger sized problem does not run with Maxima
Hah...change "Maxima" to "Macsyma" and "Symbolica" to "SMP" and that is close to a slide I remember seeing around 1980 in a presentation by Wolfram and Cole explaining why they had developed a new computer algebra system, SMP, instead of using one of the already available systems.
I don't remember the exact numbers on their slide, but same situation. Existing systems could handle the medium problems that came up in their physics research but were slow and used a lot of memory, and could not do the large problems.
