Point not addressed. Some modern flues are descended from the flue virus of 1918. There is also the bubonic plague http://www.freerepublic.com/focus/f-chat/2792352/posts and any number of bioweapon possibilities.
How ruthless a campaign do we want?
Good point. Each side would have different germs and anti-bodies.
My bet is that the Romans would have the immunity advantage, since it is their turf and they did not live in modern sanitation.
While we are at it, I believe that one could run an Abrams on alcohol. Mileage would suck.