The military of the two empires changed a great deal over the centuries even within each empire. There were more differences than similarities. The Roman story|Romans were always a predominantly infantry army, while the Byzantines were famous for their heavy cavalry.
Two similarities that I can think of are that both relied on highly disciplined and trained troops, as opposed to massive numbers or personal bravery or fanaticism. Also, they both liked to use the most modern available siege equipment, including those lighter types of balista's and catapults used in field battles.
Unfortunantely, I couldn't find that exact answer for you, but here are some interesting links on the subject.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.