because in the matter of emblems of the empire, the preview is a bit outdated, here's some info:
the eagle was NOT an official "device" of the late roman empire (after the 4-5 centuries AD up to 1453..), after Christianity was established, the legions' insignia were slowly replaced with the Christrogram (ΧΡ)... with the cross becoming more usual in the later centuries...
in what we now call "byzantine empire", the eagle in its various forms and colors, was used as a personal device for the emperor and co-emperor, for the members of the imperial family, and statesmen of the empire, and even some noble families who took the fashion of having western-like coat of arms...
the tetragrammatic cross (with the 4B's or flint-strikers (πυρέκβολα)) is used in various representations (manuscirpts, coins, etc..) since the ~10c. and in the end of the empire is the most dominant device of the empire.. it's the closest to what we nowadays could call a "national flag" (the actual use of the term being much more modern)... it appears usually in "flamoula" (horizontal type flags)....whereas the older flags were of vertical direction (banners, vexilla).. and as i said, they usually had the XP...
so, for the game, we chose the XP for the battle banner of the strat map models, because it's vertical, and for variety also... the flag appearing on the cities (when they're empty of troops) is horizontal and it's the cross with the 4Bs (and is as well as the empire's CoA...)
this flag:
is the flag of Galata... shown in some medieval portolans, this flag is the quartered version of the flags of the "Roman Empire" and the "Republic of Genoa"... it was usual for vassals or even allies, in that times to depict quartered the flags of the others...