The Holy Trinity is the end-all-be-all when it comes to combat.
The Halcyon is the best carrier in the game. It obliterates enemy SC with a back-handed slap. It buffs all ships around it. It also buffs its SC and can launch the largest swarm of SC of any ship in game. 170 at level 10. That is a FF DPS of ~300. That in and of itself is enough to make any enemy that doesn't have flak spammed quake. Then, there is Amplify Energy Aura. It decreases cooldown by 22%. Now, the average attack is a 4 second burst with a 6 second CD. By taking 22% off that 6, you'll get around 5.3... That yields around an 8% increase in damage for all advent weapons. That is great.
The Radiance is the best direct-combat ship in the game. It has the best armor, great shields, and good health. It turns damage into AM, can stop Missile Barrage in its tracks, and can cut a swath of destruction through the enemy fleet with its axial cannon. Cleansing Brilliance+Malice is better than GRG spam. Its better than Missile Barrage! CB+M=24 ships that are receiving massive amounts of damage. If you slammed the beam through 4-5 ships, that would have such an exponential increase in damage, that each ship hit by the beam, when combined with the damage of Malice would be receiving around 500 DPS for eight seconds. Nothing, not even MB trumps that kind of power. If its not a cap, it will die. And even then, that cap will be in really, really, REALLY bad shape. 4000 damage is unstoppable. Even after mitigation, this will kill anything short of a cap instantly. This ship is absolutely spectacular.
The Progenitor is just awesome. By itself, it does nothing, but with a fleet, it can launch awesome synergies. It can bring a level 10 cap back from the grave and create an army of them. It has such a powerful heal that you can just sit there and absorb Missile Barrage without even getting scratched. It has the best colonize in the game. And on top of all that, it has the best synergistic ability in the game. This ship has Malice. Malice can be combined with so many other abilities and is useful in every single one. Use it with Vengeance+Animosity, and you just made an entire fleet feel pain. Combine it with Destras and everything they have drops health at a very accelerated rate (up to around 9 DPS without even doing anything) Combine it with Cleansing Brilliance, and you have just created the most powerful attack in the game next to Safety Protocol.
Illuminators defeat just about anything the Vasari throw at them, but the TEC has no such thing. Illuminators are better than Enforcers which are their defined counter. Illuminators are arguably the best frigate in the game. Sure, the Kodiak has health, but even then, its a close match and Illums can duplicate themselves, doubling their DPS and in a sense, health. In a large group, deceptive illusion effectively increases health by 50% and DPS by 100%. That is a true force to be reckoned with.
There is no need to describe the Guardian. It speaks for itself.
These ships are what create the most awesome synergies in the game. The Vasari don't have synergies. They have individual attacks. The TEC have some synergies, but not many. The Advent can destroy entire fleets with them. Missile Barrage is good, but it won't weaken a cap to the brink of death. Cleansing Brilliance can. Cleansing Brilliance is arguably the best offensive ability in the game save for Safety Protocol. It is one of the VERY few abilities that can actually go through Shield Restore without thinking twice. When it comes to sheer power and military might, the Advent is unquestionably the best.
As far as math goes (this is especially applicable to malice synergies), Here is what I did for some of them.
Cleansing Brilliance: The target receives 250 DPS for 8 seconds. That is 2000 damage. However, if you have that beam go through 5 other ships first, they will also take 2000 damage. Throw in malice, and 30% of all that will be spread around. That means that Malice will increase your damage output by 450 DPS. Need I say more? For every ship you hit with that beam, you increase the DPS to everything else by 75. Don't mess with that. 75 DPS by itself is awesome and is Marza-esque. If you punched through 10, that is a 750 DPS buff to damage. Once again, don't make the Radiance angry. It won't work out so well... Oh, and the other thing, anything that doesn't get wiped by the beam itself would surely get destroyed by malice's overlap into the surrounding forces. Throw in another Progenitor, and you could ensure that his entire fleet gets a taste of Brilliance.
As for the Destra's ruthlessness, it automatically damages anything near it for 1.5 DPS. This is good. Let's say there are 24 ships in range. Each one receives 1.5 DPS automatically, but with Malice, it becomes 10.8 DPS. You aren't even firing at them! That kills frigates like you wouldn't believe. As long as Malice is up, enemy frigates will die, HC's will be wounded, and caps will be very unhappy. The other thing to remember is that this is passive. You just walk up to an enemy fleet and they just start dying. Not to mention that Destras have awesome DPS with their plasma cannons anyways.