O-10, the answer to the question "who is the greatest jazz composer?", as you correctly point out, should be approached from a historical perspective; and, like the essence of jazz itself, will not be entirely devoid of, at least, a certain amount of subjectivity.
This question smacks of the "KOB vs SE" debate. Is one the greatest because we happen to prefer the music on one or the other; or, is it the greatest because, in spite of our preference for one music or the other, the work had the most impact and influence in shaping the direction of the music as a whole (historical perspective). In the case of "KOB vs SE", if we remove the tendency to disqualify it because it HAPPENS to also be (God forbid!) an audiophile favorite, there is no question that KOB had infinitely more impact on the state of jazz than SE did.
There is no question that both Ellington and Mingus were great jazz composers (probably the two greatest); and both extremely influential. Interestingly, in spite of the tendency in some camps to both promote the idea that the "great unwashed" dictate what is good or not, and then conveniently abandon this agenda when it suits, I think that in this question we have a fine example of when the "unwashed masses" get it
right: Ellington reigns supreme! Ask the average music listener (even the average citizen) who Ellington was and who Mingus was. I think the results of the survey would be pretty obvious. The average person might even be able to name an Ellington tune. A Mingus tune? Unlikely.
Ellington was not only a great composer whose compositions (along with Strayhorn) have become "standards" (there's that pesky word again), he was a key influence in the development of Big Band writing which shaped an entire era, was a brilliant orchestrator who pioneered the idea of writing with the individual players' sound and style (an idea used later by Mingus); he also excelled at symphonic, gospel and soundtrack writing. In spite of all his excellence and influence, Mingus did not have such a broad scope as a musician nor composer. I think it can fairly be said that had there been no Ellington, jazz would not be quite the same today. When one considers the developmental timelines of the music during which both Duke and Mingus were active one has to wonder wether the same can be said of Mingus to the same extent. Mingus is often referred to as "the heir apparent to Ellington" and I think that pretty much sums it up.
Now, for a more subtle and potentially interesting perspective via the thoughts of Mingus himself:
http://mingusmingusmingus.com/mingus/what-is-a-jazz-composerAnd on Ellington:
http://www.npr.org/2008/11/19/97193567/duke-ellington-the-composer-pt-1
