I'm gonna have to side with Xen here.
Why? The Man-o-War sucks. Why? Because naval combat in Civ3 is good for two things:
1) Getting people places.
2) Bombardment.
You will never take a city with a ship. The Byzantine Empire, was just that, an empire, and quite a large one at that. It had a large army. Now, if you're going to represent a civilization that was known for its army, and having a large land empire, would you pick a naval unit? If so, I question your sanity. Choosing a naval unit as the unique unit makes for a worthless unique unit.
It should not be "Unique Unit" so much as "Ultimate Unit", or something that defined the civilization.
Sure, Man-o-Wars were all well and good, but if I think of the British military I thin of Red Coats. When I think of the American military, I think of probably the M1A2, not the F-15.
And when I think of the Byzantines, I think of the Cataphract, not "greek fire", which is a weapons system to begin with.
UUs should not be something "unique" to the nation so much as represent what was a military unit at that nation's greatest extent of power. I mean, hey, the Russians had a flying tank. That's unique. It's not their UU though.
In short, it just makes more sense to give the Byzantines the Cataphract out of a sense of history and fun. I know if their UU was some stupid ship I'd never use it because there'd never be a need if it didn't bombard or transport.