As for Homer, The Illiad and The Oddessy were written so far back before the period we are discussing, until we don't have any real evidence as to exactly when they were written, or in fact, that anyone named Homer even wrote the things. Herodotus told a good story, but only in a generalized way can we say that his "Histories" is really a history book. Rather, I would say it is part travellog and part fairy tales. He did tell a good story, as I said, and he did give good insight into some of the more obscure cultures of the near east. His is a great work no doubt, but one has to realize what it is, and accept it as that.
I would say that Thucydides was a more accurate and insightful historian.
Why is it a great work?