The Sova one is weak because (afaik) it only affects its own personal craft, which is usually a small fraction of carrier based fleets. My best guess is that Advent are best because of the Rapture ship and Vasari are second because of their consolidated armor/hp. But again, that's purely a guess, I don't actually know why TEC is considered weakest in that regard.

I would honestly say the they're equal in the respects that each of their special abilities seems to reflect what each race really does. However if I HAD to rank the carriers, I'd say it'd go.

Advent
TEC
Vasari

Aslo, if you ever look at the sqaudrons of a high level Halcyon Carrier their made up of about 10 to 12 fighters or bombers. Compare that to the sixe of a Sovas sqaudrons and you see the difference

yes the Halcyon carrier, does have more fighters and bombers, but we also have to look at the armor and damage increase, for the fighter and bombers, for the Sova Carrier.

Advent:

Bomber:
Damage: 34.41/AntiVeryHeavy
Hull: 75/0.15 restore
Armor: Light/1
Number per Squadron: 7 (Upgradable to 10 on Halcyon and Platform)
Time to Build: 18

Fighter:
Damage: 16/AntiLight
Hull: 40/0.15 restore
Armor: VeryLight/1
Number per Squadron: 9 (Upgradable to 12 on Halcyon and Platform)
Time to Build: 16

Platform:
Credits: 950
Metal: 200
Crystal: 110
Squadrons: 3
Orbital Slots: 6
Orbital Slots per Squadron: 2


Radiance Battleship: 0-2 Squadrons
Revelation Battlecruiser: 1-2 Squadrons
Progenitor Mothership: 1-3 Squadrons
Halcyon Carrier: 2-6 Squadrons
Rapture Battlecruiser: 1-3 Squadrons


TEC:

Bomber:
Damage: 44.400002/AntiVeryHeavy
Hull: 100/0.25 restore
Armor: Light/2
Number per Squadron: 5
Time to Build: 25

Fighter:
Damage: 19.5/AntiLight
Hull: 60/0.25 restore
Armor: VeryLight/1
Number per Squadron: 6
Time to Build: 20

Platform:
Credits: 700
Metal: 120
Crystal: 70
Squadrons: 2
Orbital Slots: 4
Orbital Slots per Squadron: 2

Kol Battleship: 0-2 Squadrons
Sova Carrier: 2-6 Squadrons
Akkan Battlecruiser: 1-3 Squadrons
Dunov Battlecruiser: 1-3 Squadrons
Marza Dreadnought: 0-1 Squadrons


Vasari:

Bomber:
Damage: 76.900002/AntiVeryHeavy
Hull: 140/0.5 restore
Armor: Light/5
Number per Squadron: 3
Time to Build: 30

Fighter:
Damage: 30.75/AntiLight
Hull: 85/0.5 restore
Armor: VeryLight/3
Number per Squadron: 4
Time to Build: 24

Platform:
Credits: 700
Metal: 120
Crystal: 70
Squadrons: 2
Orbital Slots: 4
Orbital Slots per Squadron: 2

Kortul Devastator: 1-2 Squadrons
Skirantra Carrier: 2-6 Squadrons
Jarrasul Evacuator: 1-3 Squadrons
Antorak Marauder: 1-3 Squadrons
Vulkoras Desolator: 0-1 Squadrons

All Light Carriers have 1 squadron.

All capital ships cost:
Credits: 3000
Metal: 400
Crystal: 200

My opinion is that the carriers are very closely balanced, from the perspective of fighters. Because of this, you have to take in to account the carriers' special abilities and general statistics.

I feel the Halcyon is the best carrier, because it can increase the number of fighters it has per squadron (increasing the strength of its squadrons), push all enemy strike craft away from it, it can create a cloud of additional fighters, and passivly augments all energy weapons of all allied ships near it(which is every single weapon the Advent use). I would have to place the Skirantra next, due to its heavy shields and armor, its ability to heal other ships (even though the AI is a bit buggy with it), its ability to phase fighters in and out passivly (which applies to ALL allied fighters in the area), and its ability to generate extra bomber squadrons. The Sova is a sad third to me, its only really useful ability is its embargo. Every other ability is rather limited.

EDIT: Clarified and added opinion section.

NO! 3 strike craft at a cost of 6 tac points vs 2 strike for tec/adv for 4 tac points. add in the fact you need a monster 200 metal and i believe 110 crystal vs 120/70 for tech. so at 12 tach spots you get 6 sc each, but advent costs 400/220 and tech is 360/210...

add in the fact each hanger only builds 1 fighter and 1 bomber at a time. your advent 12 tac points will be rebuilding max 4 sc at a time, vs the tech counterparts will be doing 6!! only real advantage is the 6000 hull points advent have vs the 4000 tech have... and is nearly negated with the higher repair station rate tecs can achieve (40 hp/sec vs 30/hp sec).

Advent defense is strongest with the missle defense and the anitmater regen, but their hangers are expensive and repair this craft very slow. The additional strike craft upgrades do help, but... that metal cost at 200 a pop is crazy high, no matter what stage of the game!

------------------------
as far as carrier race vs race goes... i rarely build carrier caps anyways. If I do they are number 3 sometimes but mostly number 4 or 5 capital ship built. Sova rush? you can do it if you want! after that strike craft can be tamed down with defense cruisers pretty easy, and i find the other cap ships have support abilities more in tune with my style, like the akkon/mothership/advent colony guy.

this is an old post, much of what they are talking about is out of date (by almost exactly two years)

The previous discussion is so outdated that it's effectively worthless.  All forms of carriers and hangers have been changed in successive patches since then, not to mention the changes to other units around them.