It is worth noting that Josephus' reference to the 50 years of desolation occurs in the same context where he cites Berossus:
"These accounts agree with the true history in our books; for in them it is written that Nebuchadnezzar, in the eighteenth year of his reign, laid our temple desolate, and so it lay in that state of obscurity for fifty years, but that in the second year of the reign of Cyrus, its foundations were laid, and it was finished again in the second year of Darius" (Josephus, Contra Apionem, 1.21).
This was just after Josephus quoted a lengthy excerpt from Berossus in the previous paragraph which gives the exact lengths of the Neo-Babylonian kings: "Nebuchadnezzar ... reigned forty-three years, whereupon his son Evil-merodach obtained the kingdom and ... reigned but two years. After he was slain, Neriglissar, who plotted against him, succeeded him in the kingdom, and reigned four years; his son Labashi-Marduk obtained the kingdom, though he was but a child and kept it nine months ... After his death, the conspirators got together and by common consent put the crown on the head of Nabonidus, a man of Babylon, ... but when he was in the seventeenth year of his reign, Cyrus came out of Persia with a great army ... hereupon Cyrus took Babylon" (Contra Apionem, 1.20). This history of Berossus constitute the "these accounts" in the above quote, which Josephus says agrees with sacred scripture. It is thus no coincidence that when you do the math, the "fifty years" is in accord with the length of the Neo-Babylonian period stated in the previous paragraph. What is more, Josephus then presents information from Phoenician records which gives the same length of time from the reign of Nebuchadnezzar to Cyrus, adding "thus the records of the Chaldeans and the Tyrians agree with our writings about the temple" (Contra Apionem, 1.21).
What Josephus presents in Antiquities 10.11.2 is a very sloppy paraphrase of Berossus. Here Josephus blunders the lengths of the reigns of Evil-Merodach and Neriglissar, and he erroneously referred to Nabonidus as Baltasar (i.e. Belshazzar). If you compare the two passages, it is obvious that they derive from a common source because they parallel each other in wording, but it is the latter verbatim quotation of Berossus in Contra Apionem that was more accurate.