These two nations are allies of NATO and a conflict between them would cause problems for the NATO alliance. It would be interesting which side the US, Britain, and EU would support in such a war. I don't war between these two neighbor states as ordinary Greeks and Turks get on well with each other.
I have many Turkish friends who tell me that they love Greek history and culture. They blame the politicians on both sides stoking up extreme nationalism. I love Ataturk's statement -
Peace at home, Peace in the world.