I think this is what is behind Photius' statement that Justus was a "political opponent of Josephus":
He was a political opponent of Josephus, against whom he is said to have concocted several plots; but Josephus, although on several occasions he had his enemy in his power, only chastised him with words and let him go free.
http://www.tertullian.org/rpearse/justus.htm
This information is in keeping with what Josephus says in Ant. 18.1.1 about "the madness of these men [Fourth Philosophers] towards one another, while their desire was that none of the adverse party might be left."
And in Life 9 Josephus says:
... all these persons before named gave their advice, that the city should then continue in their allegiance to the Romans and to the king. But Pistus, who was guided by his son Justus, did not acquiesce in that resolution ... Justus ... although he pretended to be doubtful about going to war, yet was he really desirous of innovation, as supposing that he should gain power to himself by the change of affairs ... . So when Justus had, by his persuasions, prevailed with the citizens of Tiberias to take arms, nay, and had forced a great many so to do against their wills, he went out, and set the villages that belonged to Gadara and Hippos on fire; which villages were situated on the borders of Tiberias, and of the region of Scythopolis.
This is the same kind of language Josephus uses to describe Fourth Philosophers, e.g., Ant. 18.1.1, War 2.13.4 and 2.17.1:
[They] exhorted the nation to assert their liberty; as if they could procure them happiness and security for what they possessed, and an assured enjoyment of a still greater good, which was that of the honor and glory they would thereby acquire for magnanimity ... in pretense indeed for the public welfare, but in reality for the hopes of gain to themselves.
These were such men ... for procuring innovations and changes of the government ...
... the violence of those that were for innovations was not to be restrained ...
And Justus was also from the Galilee region, which was a hotbed of the Fourth Philosophy.
So to me Josephus and Justus sound like two ex-Fourth Philosophers who carried their "madness ... towards one another" into the literary arena after the 66-70 CE war.