Something that is interesting, is that the Roman skirmishers have the exact same damage output as the Britons due to the fact that their hero does the exact same, they have the same upgrades and the same base attack, HP and armour. However the Romans are not nearly as used as much as Britons.
Furthermore, the Mauryan "Maiden Guards" and the Iberian "Champion Swordsman" are stronger because of the upgrade "steel working" which boosts their attack to 20.1 hack, instead of the Britons which have 18.1 hack. However the Iberians fall back as their heroes currently do not have any effects, and I am not sure just how good the healer hero that the Mauryans have when comparing to the Britons and the Romans.
Even still, the winners are still the Spartans, they are indeed the strongest champ due to the Agoge upgrade, that extra 50HP seems to actually give the champs a HUGE advantage over the Britons, test over test, making it as even as possible, Spartans win every time.
EDIT: regarding the problem on the imbalance between swordsmen and cavalry, it all depends on the way you play, I know some pros which know how to use cavalry champs really effectively. To put it very simply, cavalry is used as a hit and run unit. Its perfect when the enemies army is in the middle or busy, and you can just run into their main civ, past everything, capture something, destroy it, fall back, regain health, and repeat. This way you slowly chip away on the enemies economy without loosing almost any resources, for example, going for the traders and disrupting the trading line is EXTREMELY annoying, and if pulled off correctly, it's very effective. Note, this works well with around 20-30 of them, to make sure that they can push in and fall back as quickly as possible, this gives you space and time to build more sword champs while you distract and set back your enemy.
What would be nice is to see a bit of variation between cavalry as they are all pretty much the same, and there are no special upgrades for them (only special cavalry are the Iberian, the Roman and the Seleucid ones). Iberian being the best, due to that crazy crush damage output.