The Byzantines is a great all around civilization. They have all units and have some upgrades on ships. What the Byzantines lack is final siege units and their upgrades. Other than that, the Byzantines can use any other unit. When using the Byzantines to assalt enemy fortifications, always bring a trebuchet or two and some heavy cavalry to protect it. On sea battles, the Byzantines rule, with enhanced fire ship powers. Take advantage of the strong Byzantine structures and use defensive and offensive towers and castles. The Byzantines lack any food enhancements , so work extremely hard at the Dark Age. Also use the strong cavalry to protect your town and siege units.
Reflecting the heart of the Byzantines, the Cataphract naturally shines in the Castle Age, before the appearance of the Paladin. The Cataphract has an attack bonus against infantry, giving them an edge against such civs. One of the downers of cataphracts is their price. A paladin is cheaper and has more attack points. Use the cataphract heavily in the Castle Age because it will be one of the strongest cavalry units. Lay back on them in the Imperial Age. Cataphracts have the defined role of killing infantry.
The Byzantine tech: Logistics, gives the cataphract trample damage, like a war elephant. This allows you to use the cataphract in great numbers to break up infantry formations. You will never fear the cataphract being gangbanged on anymore! Hurl your cataphracts angainst the enemy infantry and shower them with arrows to add to the punch.