I would normally be for the protoss. But in this situation, battlecruisers would own considering both sides are fully upgraded. And even if the battlecruisers don't have yamato gun they'd still win because it takes forever for the carrier to launch interceptors attack. Also, in that patch a long time ago, the carrier's armor was weakened severely.
Battlecruisers also shoot one laser at a time while carriers use a bombardment of weak attacks, equivalent to several marines. This makes battlecruisers more suitable for killing units because attacks are instant.
Carriers however are more suitable for attacking a base, because they can launch interceptors from a far, giving them a substantial long-range advantage. Also carriers can move around while their interceptors are attacking an enemy. So in the contest of evasive maneuvers, the carrier wins.
Depends on what you mean. If you mean effectiveness in a group, then it's carriers. If you mean dogfight, then it's what pyro said: Battlecruiser wins.
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Also carriers have a number of tricks that I've found. One of course being moving and attacking at the same time. Another however is that they can literally cover the screen with their innumerable interceptors. Its cheap, but it keeps human opponents from being able to manage their units very easily because the can hardly see through the swarm.
But again carriers win only in base destruction speed and efficiency. But 12 battlecruisers vs. 12 carriers ends in a Terran victory especially with yamato gun.
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Yep the old hold position, but bc's were still faster, they shot quick bursts equal to interceptors time with 34 damage. vs an interceptors 9, but a carrier itself its easy to kill, especially with the scourge, a bc, can simply nail each one with one hit.
Yes bc's don't go down to scourges without a fight. And protoss air units as a whole are nearly defenseless. Scouts have slow moving missiles that tend to spin around in circles and carriers take forever to unload their interceptors. At the same time Terran air uses lasers and straight missiles (not gay) and wraiths can easily take on scourges from cloaking alone.