The question of authenticity has to do, primarily, with whether the passages in Tacitus and Joesphus are original parts of the text, or later additions. In the case of Josephus the scholarly consensus is that while mention of Jesus is original, some elements of the text show signs of later Christian emendation.

The second question, which is what you seem to be hinting at, is whether those texts provide any accurate account of Jesus. But both Tacitus' mentions and Josephus' are actually quite scant. They are not accounts per se. Tacitus is writing about the great fire in 64 AD, and mentions the blame put on the Christians by Nero. About all that Tacitus tells about Jesus is "suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus." (Annals 15.4)

So all that Tacitus reports is that Jesus was executed, reliably understood as crucifixion, under Pontius Pilate.

Josephus' accounts on the whole are fairly reliable. The specific overlap with Christianity occurs in three passages. One refers to the death of James the brother of Jesus. A second refers to the death of John the Baptist. The third is the most disputed, and based on internal and external evidence seems to have been altered.

Here is the text as it stands in the longest version (Antiquities 18.3.3):

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 amongst 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 from him, are not extinct at this day.

Here is the text reconstructed to omit the most probably later alterations:

Now there was about this time Jesus, a wise man. For he was a doer of startling deeds, a teacher of such men as receive the truth with pleasure. And he gained a following both among many Jews and many of Greek origin. And when Pilate, at the suggestion of the principal men amongst us, condemned him to the cross, those that loved him at the first did not forsake him. And the tribe of Christians, so named from him, are not extinct at this day.

THe reconstruction omits any suggestion that Jesus was more than human, the Messiah, or the resurrection. It tells us no more than you would expect someone like Josephus to know and believe about Jesus - a charismatic leader who performed some kind of signs, was crucified, and left a significant group of followers both Jew and Greek.