The Cybran carrier is slightly underpowered when compared to the other carriers; that is, only slightly. What it lacks in AA defense it makes up with the Cybran tactical missle 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 longer and narrower ship of the 3 carriers. Unlike the other three, it auches
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 best ship out of all the T3 carriers, because it is quite capable when dealing with other naval strike forces. It carries a good rapid-fire TMD and good sonar and radar, decent enough AA, carries an excellent artillery cannon that can bombard bases or approaching ships, 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.
Oh, one more thing: the Atlantis is a submarine. Badass.
The Aeon Illuminate also have an experimental flying carrier that is completely unlike the others, 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. Still cool to watch it reign Independence Day-style doom upon your foes, though.