So about to how big would each of the militaries be?

There's a sort of rule of thumb enunciated in The Face of Battle by the historian John Keegan that until our ~1800, a country could have a standing army of 1% of its population and up to 5% for "national emergencies".

So if you make the population of the Ahriain Empire or the Koirin Dominion around 20 million each, 200,000 soldiers at each side. Then the private side is facing less than 150,000 soldiers in total. With clever tactics and luck, victories for 3:1 on land are possible. And if the battle are in the sea, the numbers can go crazy, because the weather and the expertise of sailors are the key to many sea battles.