Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles. He was [the] Christ. And when Pilate, at the suggestion of the principal men among us, had condemned him to the cross , those that loved him at the first did not forsake him; for he appeared to them alive again the third day, as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named for him, are not extinct at this day.
Now, generally those Christians who want to defend the authenticity of this paragraph, over and against the assertion that this is a Christian insertion or at least shows signs of Christian editing, do so because such independent testimony would be important corroboration of the Christian accounts (leaving aside for the time being the manifold serious issues with Josephus as a historian). But if this really were Josephus' unedited words then the fact that a 1st c. Jew could calmly relate the fact of the resurrection and Jesus' status as messiah and yet not be himself a follower of the way actually does more to undermine Christian apologetics than help, because it would show that 1st c. Jews, even educated ones, really were credulous about such things.
It is surely more important to argue, from an apologetics perspective, that 1st c. Jews were not easily impressed by such claims and so the fact that so many of them were convinced, even to the point of martyrdom, suggests that something really did happen. If Josephus believed the account but felt it to be less than earth shattering ( it certainly had little or no impact on his understanding of the divine will in contemporary world events) then it actually weakens rather than enforces the testimony of the Christians.
As I've warned before, apologetics is a messy business with often unintended and unfortunate consequences, most of those practising it would be better off spending their time doing what Jesus commanded instead of arguing the point.