I've been using Maxima a bit recently, and I've been thinking about Axiom in comparison. I think Axiom's mathematical strengths are undeniable, but...
The Axiom community seems to be worried about the wrong things. Abstruse mathematical problems, matters relating to Aldor... and yet the interface languishes. In fact, for Windows users (who make up the bulk of computer users) there is no decent interface.
Help - Hyperdoc was all very well in its day, but now looks regressive and old-fashioned. Surely help based on HTML, or even a Windows Help interface, should be provided?
Maxima seems streets ahead in its involvement with the mathematical community. Currently there are at least two major book writing projects using Maxima: "Maxima by Example" on http://www.csulb.edu/~woollett/ and another on http://www.neng.usu.edu/cee/faculty/gurro/Maxima.html There are lots of other tutorials and documents (including one by me!) on the Maxima page. But where are the user-written Axiom books and introduction documents? The biggest one - in fact the only one available from the Axiom page - seems to be Martin Dunstan's tutorial from 1996!
A new user, scouting around for a freeware CAS, would be led to the undeniable conclusion that Axiom is simply a hobby for a few dedicated users, whereas Maxima is being developed to be useful for everybody.
The various forks: Axiom, FriCAS, OpenAxiom, also must make it hard for the new user - which one to choose, and why? The many many distributions of Linux make choosing one awfully hard for the beginner - even I, who've been using Linux exclusively for over 15 years, get confused on the rare occasions I have to install a new system. Axiom has the same problem.
Now don't get me wrong - I like Axiom very much indeed, and I will keep using it, and encouraging my students to do likewise. But I think it needs to reach more users if it is to really succeed, and for this it needs more help and tutorials, and better interfaces.