I think we would know a lot more about the Romans than the Greeks for starters. Roman history is much more embedded in oral history and tradition in modern western society than the earlier Greek.

Still we would lose a lot of knowledge on both accounts

For example, deciphering how we the Greeks worshipped and presented their religion and gods would be a nightmare. No Homer, Hesiod, playwrights, Socrates, Plato, Aristotle? Imagine how difficult understand the pantheon would be simply from temples and art. It would be a maze.

Many historical events would probably be yet to be discovered or would be less understood. For example would we know that the battle of Marathon happened? Or the whole invasion by the Persians? Maybe some archaeological evidence would point us in the direction but the stories from Herodotus and Thucydides and others wouldn't be there. How would we know what these battles were about? How would we know the outcome?

I think simple anthropological things would be easier to understand. How did the ancients live? How did the elite live? Where did their empires stretch? What did they eat? What was their currency? All of this is partly the realm of pure archaeology and we would probably still know a lot about this.

Bottom line is, ISIS can f@&k off.

I like to say that without written evidence we would probably view the relationship between Greece and Rome a bit like we do between the Hallstatt and La Tene iron Age cultures. There would undoubtedly be endless debate about why the "Romanic" culture of 100 BCE-300 CE seemed to follow from a regional Italic variant of Iron Age Hellenic culture. That aside, uniformity in material culture and artistic norms would make positing some sort of political centralization from the first century CE quite justifiable.

Which is sort if my way of saying that there are a lot of very heated debates in many other fields of archaeology that you simply don't need to have with the classical world because of the written record.