As far as I am aware the following observations were first made by Theodore Weeden (author of 'Mark: traditions in conflict') in informal email discussion.

Jesus in the Gospel of Mark

Jesus in Josephus' Jewish War
(translation of the passage below this table)

Primary subject of story is named Jesus

Primary subject of the story is named Jesus (son of Ananias) [Jewish War, 6, 300]

Jesus is an artisan (Greek 'teknon', or translated 'carpenter'). (The artisan class ranked below peasants) [6:3]

Jesus is described as a low class unskilled rustic peasant [J.W.6:301]

Jerusalem leaders believe Jesus is demon possessed [3:22]

Jerusalem leaders believe Jesus is demon possessed [J.W.6, 301]

Some people thought Jesus was out of his mind [3:21ff]

Some thought Jesus was a maniac [J.W.6,305]

Jesus was at times teaching daily in the Temple [14:49]

Jesus was daily in the Temple repeating his message [J.W.6,306]

In the Temple during time of a holy festival (Passover) [14:2]

In the Temple during the time of a holy festival (Tabernacles) [J.W.6,301]

Jesus cites Jeremiah 7:11 (LXX, speaking against defilement of Temple) (conflated with Isa.56:7) to denounce practices in the Temple [11:17]

Jesus cites Jeremiah 7:34 (speaking against the people of Judah and Jerusalem) in his harangue against Jerusalem, the Temple and the people. [J.W.6, 301]

Declares Woes on the people of Jerusalem/Judea [13:17]

Declares Woes on the people of Jerusalem/Judea [J.W.6,304,306,309]

Pronounces doom on the Temple [13:2]

Pronounces doom on the Temple [J.W.6,300,309]

Arrested by the Jerusalem leaders [14:43]

Arrested by the Jerusalem leaders [J.W.6,302]

Accused of speaking against the Temple [14:58]

Accused of speaking against the Temple [J.W.6,302]

Made no defence for himself in face of these charges of speaking against the Temple [14:60f]

Made no defence for himself in face of these charges of speaking against the Temple [J.W.6,302]

Physically abused at the Jewish hearing [14:65]

Physically abused at the Jewish hearing [J.W.6,302]

Following Jewish hearing the Jerusalem authorities delivered him to the Roman procurator (Pilate) [15:1]

Following Jewish hearing the Jerusalem authorities delivered him to the Roman procurator (Albinus) [J.W.6,302f]

Interrogated by the governor (Pilate) in the Roman hearing [15:2-4]

Interrogated by the governor (Albinus) in the Roman hearing [J.W.6,305]

During their Roman interrogation the governor asks him to disclose his identity [15:2]

During their Roman interrogation the governor asks him to disclose his identity [J.W.6,305]

He is silent before governor [15:3-5]

He is silent before governor [J.W.6,305]

The procurator moved to release Jesus (but failed) [15:6-15]

The procurator moved to release Jesus (successfully) [J.W.6,305]

Jesus was scourged at end of his Roman hearing [15:15]

Jesus was scourged at end of his Roman hearing [J.W.6,304]

Killed by Roman soldiers [15:16,20-24]

Killed by Roman soldiers (although unluckily by chance) [J.W.6,308-9]

Uttered a personal woeful cry just before his death [15:34]

Uttered a personal woeful cry just before his death [J.W.6,309]

Died with a loud cry [15:27]

Died with a loud cry [J.W.6,309]

Mark uses the word "naos" for Temple in the contexts of the charge against Jesus that he spoke against the Temple [14:58; 15:29; and the vindication of Jesus' dismissal of the Temple in 15:38]. Elsewhere Mark always uses "hieros" for the Temple [11:11,15,16,27; 12:35; 13:1,3; 14:49]

Josephus uses the word "naos" for Temple in the account of his Jesus' declarations against it. [J.W.6,301,309]

 
G. A. Williamson's translation of Josephus' The Jewish War (pp.327-8, Penguin Classics, 1959)
An incident more alarming still had occurred four years before the war at a time of exceptional peace and prosperity for the City. One Jeshua son of Ananias, a very ordinary yokel, came to the feast at which every Jew is expected to set up a tabernacle for God. As he stood in the Temple he suddenly began to shout: 'A voice from the east, a voice from the west, a voice from the four winds, a voice against Jerusalem and the Sanctuary, a voice against the bridegrooms and brides, a voice against the whole people.' Day and night he uttered this cry as he went through all the streets. Some of the more prominent citizens, very annoyed at these ominous words, laid hold of the fellow and beat him savagely. Without saying a word in his own defence or for the private information of his persecutors, he persisted in shouting the same warning as before. The Jewish authorities, rightly concluding that some supernatural force was responsible for the man's behaviour, took him before the Roman procurator. There, though scourged till his flesh hung in ribbons, he neither begged for mercy nor shed a tear, but lowering his voice to the most mournful of tones answered every blow with 'Woe to Jerusalem!' When Albinus -- for that was the procurator's name -- demanded to know who he was, where he came from and why he uttered such cries, he made no reply whatever to the questions but endlessly repeated his lament over the City, till Albinus decided he was a madman and released him. All the time till the war broke out he never approached another citizen or was seen in conversation, but daily as if he had learnt a prayer by heart he recited his lament: 'Woe to Jerusalem!' Those who daily cursed him he never cursed; those who gave him food he never thanked: his only response to anyone was that dismal foreboding. His voice was heard most of all at the feasts. For seven years and five months he went on ceaselessly, his voice as strong as ever and his vigour unabated, till during the siege after seeing the fulfilment of his foreboding he was silenced. He was going round on the wall uttering his piercing cry: 'Woe again to the City, the people, and the Sanctuary!' and as he added a last word: 'Woe to me also!' a stone shot from an engine struck him, killing him instantly. Thus he uttered those same forebodings to the very end.
 
The Whiston translation of Josephus' War of the Jews (6.300-309)
But, what is still more terrible, there was one Jesus, the son of Ananus, a plebeian and a husbandman, who, four years before the war began, and at a time when the city was in very great peace and prosperity, came to that feast whereon it is our custom for every one to make tabernacles to God in the temple, began on a sudden to cry aloud, "A voice from the east, a voice from the west, a voice from the four winds, a voice against Jerusalem and the holy house, a voice against the bridegrooms and the brides, and a voice against this whole people!" (Jer.7:34 LXX) This was his cry, as he went about by day and by night, in all the lanes of the city. However, certain of the most eminent among the populace had great indignation at this dire cry of his, and took up the man, and gave him a great number of severe stripes; yet did not he either say any thing for himself, or any thing peculiar to those that chastised him, but still went on with the same words which he cried before. Hereupon our rulers, supposing, as the case proved to be, that this was a sort of divine fury in the man, brought him to the Roman procurator, where he was whipped till his bones were laid bare; yet he did not make any supplication for himself, nor shed any tears, but turning his voice to the most lamentable tone possible, at every stroke of the whip his answer was, "Woe, woe to Jerusalem!" And when Albinus (for he was then our procurator) asked him, Who he was? and whence he came? and why he uttered such words? he made no manner of reply to what he said, but still did not leave off his melancholy ditty, till Albinus took him to be a madman, and dismissed him. Now, during all the time that passed before the war began, this man did not go near any of the citizens, nor was seen by them while he said so; but he every day uttered these lamentable words, as if it were his premeditated vow, "Woe, woe to Jerusalem!" Nor did he give ill words to any of those that beat him every day, nor good words to those that gave him food; but this was his reply to all men, and indeed no other than a melancholy presage of what was to come. This cry of his was the loudest at the festivals; and he continued this ditty for seven years and five months, without growing hoarse, or being tired therewith, until the very time that he saw his presage in earnest fulfilled in our siege, when it ceased; for as he was going round upon the wall, he cried out with his utmost force, "Woe, woe to the city again, and to the people, and to the holy house!" And just as he added at the last, "Woe, woe to myself also!" there came a stone out of one of the engines, and smote him, and killed him immediately; and as he was uttering the very same presages he gave up the ghost.
Neil Godfrey
2006
http://vridar.org