Regarding how you can counter Guardians from the TEC standpoint. Stock up on the light frigates, and research the anti-antimatter ability. They will eat right through the Iconus antimatter, leaving them useless.
Toss in a few Cielo Cruisers additionally in any anti-Advent fleet, as Astax mentioned. Their Focus Fire ability helps against the Advent's heavy shielding.
So the Cielo Command Cruiser and Stilakus Subverter are both Advent-killer cruisers - the Cielo focusing fire on shields to eat them away.
The Subverter, though, would be giving ALL Vasari weaponry a 25% boost in their chance to penetrate shields. So even their Flash Beams and Pulse Guns would be able to cut through once in every four shots, while Phase Missiles would be flying around as if there was nothing there to stop them at all. Kanrak Assailants would obviously take the role of staple 'infantry' frigates being stronger, better optimized, and longer ranged than Ravastra Skirmishers while taking less supply slots, being cheaper and quicker to build.
But what Capital ships the Vasari would bring is a slight problem. A Skirantra Carrier would be obvious for it's hull-repair service and defense against bombers. The Antorak Marauder would be a no-brainer because of Phase Out and it's portable Phase-Gate ability. The choice for a direct-combat cap-ship would between the Kortul Devastator and Vulkoras Desolator.
The Devastator would have a strikecraft squadron and it's Disruptive Strikes antimatter-killer ability at lower levels, would get Volatile Nanites at higher levels, and would have better armor, more defensive guns, a tougher hull, and stronger shields(all of which are normal characteristics of battleships).
The Desolator, on the other hand, would have Phase Missile Swarms at lower levels, a strikecraft squadron at higher levels, very strong siege capabilities, and a far stronger front-end Phase Missile attack.
It would kill Advent cap-ships in a blitz manner but get battered if something goes wrong. The Kortul would have a slower approach with much weaker Phase Missile armament and would need Subverter support to help get it's main Beam shots past Advent shields.
Sheesh. Just give up. You'll never beat the unity. Stop resisting and join us in the light.
OT: Kill the mothership first. It's your number one target. Ignore everything else but the mothership. The Advent progenitor is the king of its fleet and it holds everything together. Unless you're a missile dependant Vasari hack, you're not going to do any real damage to an Advent fleet until you down that sunovagun.
In fact, if you see more than one level 6+ mothership: all your base are belong to us.
The Progenitor Mothership is actually quite lousy in it's own armament, with somewhat heavy broadsides and pathetic frontal armament, and worse shielding and armor than other Advent cap-ships. It would be focused on it's 3 abilities, and it would be easy for bombers(esp.), Assailants and Desolators to punch holes through it. Or it could get pounded by Disruptive Strikes to take out it's antimatter, or just be Phased Out of the battle and allowed back in when everyone else is dead or have run away.