Polybius, on the absence of any other contemporary source and on the fact that he wasn't roman neither carthaginian, is indeed the most reliable source, even if working for the romans. His greek passion in the search for truth visiting personally the places and routes Hannibal took, collecting physical evidences like those plates where Hannibal wrote his army's numbers and taking testemonies from people from those same places is remarkable. He even later in his life followed the steps of Hanno the Navigator sailing along the Moroccan and Mauritanian atlantic coast.
Livy on the other hand was a much more passionate and biased born latin, besides writing at a much more distant time. However, since Polybius account of the 2nd punic war became fragmented after Cannae, we are left with none other than Livy for the most part of events since his work remains fully preserved. What is positive though is that one of Livy's main source regarding the 2nd punic war was Polybius and both their narratives, up to Cannae, are oftenly carbon copies. So we can assume that Livy's account post-Cannae should not be taken entirely with "a grain of salt" as moonburn suggests. Livy even had an advantage as he used more sources, including a very important one, Coelius Antipater, who followed Silenos, one of the historiographers who accompanied Hannibal during his campaign and who was also used by Polybius. Coelius wrote about the second punic war in 7 books, who are now unfortunately lost. In this way Hannibal's quotations like the one I presented are very possibly true, or at least, very close to his actual words.
When reading Livy you must distinguish the parts where he makes judgements of character, personal opinions and engrandment of anything that would embolden his own nation, from facts and quotations from older sources he could not alter much due to the distance in time that separated him from these events. Most of the critics about Livy are regarding his early works about the foundation of Rome where almost no sources were available and he gave his imagination a lot of wings. Being contemporary of Augustus and his period of success as well as the brink of the Christian Era helped emphasize his works.
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