1. Go carriers yourself, build fighters, and research the crap out of phase missiles. He will have more fighters because he is Advent, but your fighters will hit alot harder, and you will be able to field 3 carriers for every two of his cause Drone hosts are pricy. You can ignore his fighters and go mostly bombers too, if you want. Vasari bombers are tough, and if you have enough of them you will destroy his drone hosts before the drones reduce your bombers...
2. If he is only building drone hosts you can counter with light frigates. You want 3 for every one of his carriers. Research regeneration and chase his carriers down. If you want bring in some flak and research Charged missiles, but you are going to need an aweful lot to make a dent in his strikecraft.
3. Get Vasari Cap Carriers and Battleships. Both have abilities which should give your strikecraft an advantage.
