This is an interesting but complex question. It's complex for a couple reasons. One, it was very easy to make a mistake in transcribing Greek and Latin numbers when copying a manuscript, meaning that the numbers that we have in our modern editions of texts may be very far off from the numbers that ancient authors wrote. Two, different ancient historians and authors had different methods for compiling battle numbers or for exaggerating them. Some might have just copied what they found in the histories they were drawing on, some did their own research on numbers with great fastidiousness, citing primary documents. Polybius 3.33 provides an example; here he defends the precise troop numbers he gives for Hannibal before he crossed the Alps, citing an inscription of Hannibal's near Croton in Italy and criticizing authors who try to make their misstatements about numbers plausible. Others will likely have gone for what you call the symbolic mistake; I'm inclined to think that Herodotus' inflated calculation of the size of Xerxes' army is an example of this. Even if Herodotus is not an example of this, later Greek authors who knew Herodotus definitely emphasize that Xerxes' army was so large to be uncountable (Xen. Anab. 3.2); they view his numbers as symbolic. We can compare that to Herodotus' very precise number of Athenian and Platean casualties at the battle of Marathon: 192 Athenians and 11 Plateans. Whether these numbers are accurate or not, the attention to precision is interesting, showing both that Herodotus is doing something different here than when he counts Xerxes' army (or Darius' at Marathon, for that matter) and that the Athenians and Plateans themselves were clearly attentive to individual casualties.

But the reasons for inflated numbers are often more complicated than manuscript error or authorial exaggeration can account for. To focus on the Romans during the Republic, they often had no idea how many enemies they were fighting in a battle; who was going to provide an accurate count? It was therefore easy for competing numbers to arise, as generals tried to claim that they had defeated large numbers of enemies so as to secure a triumph, with their rivals perhaps denigrating the numbers in turn (Miriam Pittenger's excellent 2008 book, "Contested Triumphs," pp. 104-114 has a great analysis of debates over battle casualties in the second century B.C.). These different numbers could then be passed on in different ways: through inscriptions, family records, oral traditions, historiography (Liv. 8.40 on competing historical traditions). How easy would it be for an ancient historian a century or more later to get the right number? And how would they even begin to get the right number for periods which had no reliable historical sources?

There's a great passage from Livy (6.12) that addresses these problems. After narrating a series of Roman wars against the Volscians and Aequi in the fifth and fourth centuries B.C., he notes that it seems impossible that these two peoples continued to have soldiers, given how many troops Livy's sources say the Romans repeatedly killed and enslaved. Livy comes up with a bunch of possible justifications, but it's pretty clear that he knows that these exaggerated numbers make no sense. Perhaps then, we can say that this doubt points to Livy's knowledge that many of the numbers he cites are "symbolic."

I'm not sure I answered your question in the way you may have wanted someone to, but I hope I have shown why it may be more complex than determining whether an ancient author is inflating numbers out of a desire to exaggerate or for symbolic reasons. Different authors had different methods for dealing with numbers, and they dealt with battle numbers in different ways in different parts of their texts. Assuming you have the number the author intended when you pick up your edition of their text, it takes close reading, contextualization and hopefully a few meta-passages (like the Polybius and Livy ones I cited above) to get some feel for why they're using numbers in the way they are.