Which 'Josephus' is Closer to the Original? Pseudo-Hegesippus Book 3 Chapter 15 or Bellum Judaicum Book 3 Chapter 8?

Now to continue our ongoing comparison between parallel sections of Pseudo-Hegesippus and Jewish War. As noted both traditions had strong chronological parallels with Vita up until this point. If read chronologically Vita implicitly argues that the massacre at Gamala and Sepphoris occurred under Josephus command of Galilee. It can be inferred that there was an original tradition that Josephus originally fled with the Jewish rebels and continued to have a leadership position until the siege of Jerusalem. One might assume that like the 'John' of the rabbinic tradition he was captured in the early stages of the revolt and acknowledged that the true messianic interpretation of Genesis 49:10 was that Vespasian was the awaited world ruler then. 

In any event since Hegesippus and Jewish War agree that Josephus capture happened at this point in the shared narrative, the claim must have been developed rather early.

The next section following the last citation of the narrative in Hegesippus reads:

Josephus meanwhile in a certain cistern was hiding among the glowing ashes of the city, not all unaware that as the leader of the opposing forces he was being zealously sought for. Having come out on the second day, when he noticed that everything was encircled, he returned into the cistern. On the third day a certain woman found out revealed to those seeking him that the hiding places of Josephus were known to her. But in the cistern also forty men who had fled there were hiding themselves. Who when they noticed Josephus to be summoned out by Vespasian in the hope of safety first through Paulinus and Gallicanus, afterwards through Nicanoris, who was bound to Josephus by virtue of ancient friendship, and for that reason sent that he should give a pledge, he willingly carried out the obligation of the assigned task, having surrounded Josephus they addressed him with words of such kind. [Pseudo-Hegessipus 15]

The parallel (and much, much longer section) in Jewish War reads:

And now the Romans searched for Josephus, both out of the hatred they bore him, and because their general was very desirous to have him taken; for he reckoned that if he were once taken, the greatest part of the war would be over. They then searched among the dead, and looked into the most concealed recesses of the city; but as the city was first taken, he was assisted by a certain supernatural providence; for he withdrew himself from the enemy when he was in the midst of them, and leaped into a certain deep pit, whereto there adjoined a large den at one side of it, which den could not be seen by those that were above ground; and there he met with forty persons of eminency that had concealed themselves, and with provisions enough to satisfy them for not a few days. So in the day time he hid himself from the enemy, who had seized upon all places, and in the night time he got up out of the den and looked about for some way of escaping, and took exact notice of the watch; but as all places were guarded every where on his account, that there was no way of getting off unseen, he went down again into the den. Thus he concealed himself two days; but on the third day, when they had taken a woman who had been with them, he was discovered. Whereupon Vespasian sent immediately and zealously two tribunes, Paulinus and Gallicanus, and ordered them to give Josephus their right hands as a security for his life, and to exhort him to come up.

So they came and invited the man to come up, and gave him assurances that his life should be preserved: but they did not prevail with him; for he gathered suspicions from the probability there was that one who had done so many things against the Romans must suffer for it, though not from the mild temper of those that invited him. However, he was afraid that he was invited to come up in order to be punished, until Vespasian sent besides these a third tribune, Nicanor, to him; he was one that was well known to Josephus, and had been his familiar acquaintance in old time. When he was come, he enlarged upon the natural mildness of the Romans towards those they have once conquered; and told him that he had behaved himself so valiantly, that the commanders rather admired than hated him; that the general was very desirous to have him brought to him, not in order to punish him, for that he could do though he should not come voluntarily, but that he was determined to preserve a man of his courage. He moreover added this, that Vespasian, had he been resolved to impose upon him, would not have sent to him a friend of his own, nor put the fairest color upon the vilest action, by pretending friendship and meaning perfidiousness; nor would he have himself acquiesced, or come to him, had it been to deceive him.[Jewish War 3.8.1,2]