Yes it's quite diverse, although its not as diverse as you might think. Generally the only type of army you use is the phalanx based ones.
The only time I use non phalanx armies is when I'm short of troops or I create mercenary armies
With Carthage you can have phalanx armies, hoplite armies, heavy infantry armies or a mixture of the three (with assault infantry)
Still I like seleukids more, cause its got the strongest units in the game.
It has a larger variety of units but still only one type of army
Regarding the Romans, have you reached the east yet? Macedonia and Epirus tend to spam really weird units in their armies until they are richer. So you might not be facing the full might of phalanx nations. When you get to the east, you will face the infamous silvershild and klerouchi phalanghites spam. Then the casualties in each battle will begin to be felt. Romes cavalry roster is quite poor for most of the game. Mercenary cav isn't as good as the factional cav of most nations that field cavalry.
The best you can get is probably the Thessalian cavalry and those are barely a match for the prodomoi of the Hellenic kingdoms (unless they are using them really stupidly)
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