Robert E. Van Voorst gives a scholarly overview of the evidence for the historicty of Jesus from the works of Josephus.
Robert E. Van Voorst, Jesus Outside the New Testament: An Introduction to the Ancient Evidence (Grand Rapids, Mich.: Eerdmans, 2000), 81-104
If the neutral reconstruction of the Testimonium is correct, what information does it give us about Jesus? Given the hypothetical nature of the reconstruction, we must be cautious about drawing conclusions. Nevertheless, significant information about the life of Jesus emerges. First, and most apparently, it (along with the later mention of Jesus at Ant. 20.9.1 §200) affirms the existence of Jesus. If any Jewish writer were ever in a position to know about the nonexistence of Jesus, it would have been Josephus. His implicit affirmation of the existence of Jesus has been, and still is, the most significant obstacle for those who argue that extra-biblical evidence is not probative on this point.
Second, Josephus calls Jesus by his correct, personal name. That he does not add "of Nazareth" may conform to the Roman readership of his book, for such a common New Testament and Jewish description would have little meaning for them. Moreover, he does not use "Christ" as a name, just as he avoids it as a personal name in Ant. 20.9.1 §200.
Third, Josephus's testimony loosely corroborates the New Testament's dating of Jesus, his death, and the first church. "About this time" places Jesus' ministry and death, and the continuation of his movement, in the governorship of Pilate. Further precision cannot be obtained from this general phrase, which Josephus seems to prefer (cf. the beginning of the next section, "About the same time..."). Given the confusion of some rabbinic writings about the century in which Jesus lived, Josephus's accuracy is significant.