A fleet of comparable size filled with counter units will do... just look at the damage types. Bring in enough anti heavy to destroy the repair cruisers, i would use a big bunch of disciples or cobalts, both upgraded with the special abilites. And the rest heavy cruiser combined with support ships ( hoshiskos, iconus, subverters ).
That will do.
Send the light frigates to hunt down the repair cruisers. Drain antimatter or disable reator will deal with them so they cant do anymore healing even before they are all killed.

The opponent might perceive them as a main threat and the best target for the lrm ( after your cap probably, just retreat instantly with the cap before loosing it ).
Send in the HCs to kill of the LRMs.
Id say the key is to neutralise the hoshikos fast. The rest will fall in time to the counter units.

As vasari get subverters and stun them. I bet the come in a nice big blob

If you're playing Vasari, you need to get with the Subjugator. It is the most powerful single unit in the game and a couple of them will disable his whole fleet. As Advent, again, you should be able to kill him with ease if you have a comparable fleet. Tec is the weakest faction per capita. Malice with a bunch of illums and guardians will make short short work of him.

for vasari its called the subverter.