Did ancient civilizations have variety in there styles of art?

One way to easily divide schools of art is to think about who was paying to train the artists and who was commissioning artistic works. When the State (and especially the State Religion) is responsible for artistic education and expression, you often find a 'right way' of doing things that doesn't change much over time. Who is going to build a tomb or a temple that fails to comply with the officially sanctioned way of doing things? That's where you find Egyptian and Mesopotamian art is often very static and compliant with an accepted norm.

You find more cross-pollination of art in port cities: Tyre and Carthage, for instance, do not have distinct domestic styles so much as an amalgam of what the wealthy Phoenicians liked best in the art of their trading partners.

When you look at Greek Art, you see a pretty steady march of innovation from one generation to the next. Think how many schools there must have been for artists in Greece? Most city-states would have had more than one, and each master would have brought up his pupils in the latest style most likely to win paying commissions from a fashion-conscious and competitive clientele of both government and religious bodies, and also many wealthy private citizens.

For all that, I am of course speaking in generalities: Egyptian and Mesopotamian state-sponsored art does have examples of innovation and cross-cultural borrowing; trade-based economies did have domestic art, and the Greeks did have official formulas that they were loathe to abandon quickly (try drawing some kouroi on graph paper and play spot the proportional ratio formula. You'll think you're on the Nile!). Still, I hope this speaks to your question a little bit.

Mods? I am not at home at the moment. I will edit my comment to include sources in an hour or two.

EDIT: Sources. I've just gotten home, and I'm casting an eye over my bookshelves to see what would back me up. I didn't really get into too many specifics. I suspect Broadbank's The Making of the Middle Sea would support everything I've said, but for the sake of rounding it out I should mention Osborne's Archaic and Classical Greek Art, Aubet's The Phoenicians and the West, and White's Everyday Life in Ancient Egypt.