Alexander army - are make up of foot soldiers - Phalanx &
shield bearers , cavalry - a very good balance force , but more on
close quarter combat.
Genghis khan - however is more on light cavarly. which is more on
arrows, they have 2 blows one for fast shooting and one for long
distance. Usually they engage enemy in long distance shooting. The
range of their arrows which is armour pericing is over 500m to 600m
they can penterate the roman shields and armour easily. Usually
each man will have 2-4 horse each so they can ride long distance.
Also usually they will pretent to retreat and attack later, which
their mobility enable them.
I view of this I guess Alexander army is the strongest if face on
and in close combat fight. But in the end , I think if the Mongol
refuse to get engage in close combat, but with range weapons and
mobility, they should have the advantage over Alexander army.