Most European people know about Odysseus, but few have read Homer, even in translation.

I one met a visiting Iranian academic just after I'd learned about the Shahnameh. I'd also read the opinion of a French scholar who thought its language was, for a modern Iranian, like Montaigne for a modern French. The Iranian woman told me that very few people in Iran actually read the book. It's very long, and hard to grasp for untrained readers. But most people know some of its stories and characters, because they are often mentioned in everyday life, and because the abridged prose books are widespread.

BTW, I don't know which editions are the most popular in Iran. Wikipedia says the Shahnameh was heavily modified and modernized up to the 14th century, when its most famous illustrated edition was created. The book most read today is probably not a scholar edition.