Maces will face his Hwachas, as they give a 50% bonus against Melee units
The Horse Archers will attack him, he won't need to attack them, thus they'll face his spears.
Asoka may have longbows, but if he's been peaceful so far, he shouldn't have any that have more than 2 city garrison promotions, so his Hwachas should be able to take that kind of a defensive stack pretty well.
Now, he probably can't take Delhi, but I'm sure he can take most, if not all, of Asoka's bordering cities.
Especially if he pulls a trick I learned recently...kill all but 1 wounded defender in a city, then let the AI reinforce the city....then smack it again. Do that a couple times, and the AI will have very few troops left for anything else.
Another note, Harbourboy...is that if you take a city, but don't think you'll be able to keep it...then just raze it unless it has a wonder or shrine in it. That way, even if you don't win the war, you still hurt Asoka.