There are three Tech 3 and two Experimental aircraft carriers. They are used to build, store, repair and deploy aircraft and be a large, hard to sink anti-aircraft platform.
The Cybran carrier is slightly underpowered when compared to the other carriers; that is, only slightly. What it lacks in guided AA defense it makes up with the Cybran tactical missile defense, a nearly flawless TMD compared to the other factions' TMDs. That being said, the Command Class is still named 'Command' for a reason; unlike the other carriers, its aircraft are often needed to be its saving grace in an attack. It is also known to be the longest and narrowest ship of the T3 carriers, and launches its aircraft from its bow, unlike the others.
The Aeon carrier is a fairly decent ship by anyone's standards, but its larger width may prevent it from reaching desireable areas, and leaves a huge target for torpedoes. What it lacks in naval defense it makes up with having the best AA defense compared to the other carriers; this ship is often used to combat Soul Rippers over the sea (because it has high health, its missiles do high damage and can never miss, and it can summon forth T3 Air Superiority Fighters to aid it in combat).
The Seraphim carrier is most likely the most versatile ship out of all the T3 carriers, because it is quite capable when dealing with other naval strike forces. It carries a rapid-fire TML and excellent sonar and radar, decent enough AA and can summon aircraft to aid it in times of desperation. That said, do not attempt to bring this ship along with a naval strike force; it is much better used near the base as a mobile, defensive air staging platform, and would most likely get destroyed in a strike force or slow the force down because of its bulky size.
The UEF carrier is very different from the other three (though not as much as the CZAR) because it is an Experimental unit, not a Tech 3 unit. It is armed with four Flayer SAM Missile turrets and several very high-quality torpedoes, as well as far superior health at 40,000, 4x build speed and consumption compared to a T3 factory, and the ability to carry a truly ludicrous 150 aircraft! To top it all off, it has almost half the unassisted build time of the other T3 aircraft carriers. The only real downside to the Atlantis is that it costs over three times more mass and energy than its equals, though it is still cheaper than any other T4.
The Atlantis is also submersible with one the best torpedo systems in the game, making it highly deadly when it is loaded with aircraft, and nearly unstoppable save for nuclear weapon if multiple are deployed.
The Aeon Illuminate also have an experimental flying carrier, the CZAR. It has AA capability and its quantum beam generator packs a powerful punch, but its vulnerability to ASF attacks even when escorted by ASFs of its own makes carrying aircraft inside it a risky proposition. Its high vulnerability, inability to be repaired without borrowing units from another faction, and equally high crash damage means that the vast majority of CZARs fly one-way missions. One rather ineffective way to use the CZAR's crash weapon to take out an any commander or base. Since the CZAR is repairable except self-repairing, it might be best to let the experimental die over water or far away from the enemy base as possible. The mass from a crashed CZAR is more than enough to kick-start any-type of counterattack.