Varangian Guards take two turns to produce. While the Byz are taking those two turns to build that unit, a European faction could build two units.

So don't forget to take into account build times. Varangians are good, but they're not game breakers in single-player.

I'm disappointed to hear that Lancers can beat Kataphractoi. I have a soft spot for the Byz. (Read "Agent of Byzantium" by Harry Turtledove. It asks the question, what if Mohammed had picked up Christianity, become Saint Mouamet, the patron saint of change, and Islam never toppled the Persian Empire? In the book, a soldier with a knack for finding uses for inventions goes on a variety of missions. Also, the Swords of the Legion quartet was good. So was the Krispos trilogy. The quartet dealing with the pseudo-Byzantine/pseudo-Persian conflict and the invasion of the pseudo-Turks, though, give it a pass...)

Anyway, ARE the Kataphractoi and the Pros. Allagion the top cavalry for the Byz? What about late game?