The Revelation isn't that big a threat, it has some decent abilities (Vengence and Vertigo aren't bad) and at it's highest levels it can steal your Frigate/Cruiser class ships, which is more than a little annoying. But if you want to kill one of them, using a good number of Javelis LRMs or Kodiak Heavy Cruisers will get the job done.

The Disciple is a decent little unit, but ideally you don't want to use Cobalts to fight them since that's more like fighting rock with rock. What you want to do is use Javelis LRMs against Disciples (and enemy Cobalts or Skirmishers). They will really tear up Disciples for the cost.

The Defense Vessel is Advent's flak, it has a lot of hitpoints and does a decent amount of damage to lighter targets. Javelis LRM's don't work too well against them, ideally you should use Cobalts to fight them, since they will have trouble doing much damage to the Cobalts with their damage and armor types.

Illuminators are a big problem for TEC, they're the rough equivalent of TEC's Javelis, but come later in the game, are more expensive, but are considerably better. Your best bet against them is to go for Kodiak Heavy Cruisers, or get a good number of Javelis LRMs before the Illuminators start to mass, since once they get in groups they are big trouble. Illuminators can be vulnerable to bombers, but for the cost of carriers and how long it takes for them to kill enemies (especially if the Defense Vessels are still alive) it generally isn't such a great plan.

The Destra Heavy Cruiser is a mean unit as well, TEC's best bet is usually just producing Kodiaks and Hoshikos to fight them, since TEC's superior economy should allow them to outproduce an Advent that goes heavy with them. Heavy Cruisers are also vulnerable to Bombers, but the cost of carriers makes strike craft strategies iffy.

The Sentinel is the Vasari flak unit, it can be countered by Cobalts fairly well, as well as Heavy Cruisers.

A suggestion ... if your worried about the fighters invest in the Kol battleships flack ability, get a chunk of flak cruisers (against computer advent I like to have 15 or 20 of them for a mid sized fleet), and get some fighters... the secret about Advent fighters is there are a lot of them but they are made out of paper... like a fleet of Origami Cranes. There are about 7 to 9 bombers/fighters in a squadron with a handful of health each. If you have a Kol or 2 and your own fighters you can kill a lot of them particularly if you back them up with plenty of flak... I just add in the fighters because they are quite effective particularly if the Advent fighters have damage from the Kol and flak.

The computers reliance on fighters can also be their down fall. I love strike craft but once you shoot them all down all those cool drone carries are just hunks of metal. Make sure you don't waste a lot of time shooting them after that unless all the stuff that shoots back is dead already... once you have the counter in place it works over and over so no need to worry about them... and all the things you used in the counter can be used against particularly the Illuminators (namely fighters and flak).

Also note that many of the problems your having killing Advent units are compounded by the combo of Iconus Guardians and Domina Subjugator. The Domina is repair and the Iconus basically shares damage with near by units which it absorbs mostly on its shields (which are capital ship class shields). If you can find a way to disable particularly the Iconus this will help you a lot. If I can I some times try to focus fire these right off the bat... a lot of fighting I just monitor the computer and make adjustments to its choices to fit the situation but in the case of these annoying units I try to kill a portion of them early or disable/drain their anti matter.

As to the Revelation Battlecruiser I was under the impression that was the Siege Cap for Advent and that Redmaw's description above was for the Rapture Battlecruiser. I could be wrong though...