Lords of Shadow is an Epic, a Tragic Epic, of epic proportions.
God of war is a revenge story of Epic proportions, but it is not an epic.
Music actually sucks on both of em, "epic" music sounds good, but it usually shamelessly recycles a small amount of tracks and overall forgetful since none of the music follow a specific melody.
God or War uses Greek Mythology, but follows it with a grain of salt, me being a fan of a few great greek story which is heavy on the Gods, God of War 3 is the one that pisses me off the most since it defies its own logic it has set up in many ways.
Lords on the otherhand is usually built on multiple mythologies and movie mytholoy, its major flaw is poor execution of really engaging you into the story.
Since I am ratiung them completely separate, Lords Wins due to having Epic proportiions and as well as an Epic form of story which ends in Tragedy.