Since armour is significantly more important to the period, I'd expect four dice for mediums and heavies, but heavies can handle additional damage. Whether that's through ignoring the first crossed sword result, having an additional block or whatever remains to be seen.
In Command and Conquer Ancients, I was thinking of making a house rule that all Heavy Infantry would attack with 4 dice, just like Medium Infantry, and they take(immune) no Cross Swords damage due to their heavier armor.
Maybe this is the concept of wearing heavy armor verse medium armor? Plate verse Chain?