The Aeria Drone Host, and the other Carrier Cruisers require antimatter to construct their Strikecraft wings (about 8 Antimatter for each fighter, 18 for each Bomber). This usually isn't noticed though because upon construction they have considerable Antimatter stores which they can use to load up on their ships. During prolonged battle though this can be noticeable, because when they're out of Antimatter ship production becomes very slow. For the fun of it.
Vasari Lasurak Transporters pay about 18 Antimatter for each fighter, and have 3 fighters in a wing (72 antimatter total). Each Vasari Bomber costs 42 Antimatter and there are 3 bombers in a wing (126 antimatter total). With a build time of 25 seconds for each fighter and 30 seconds for each bomber it takes 100 seconds to complete it's bombers and 90 seconds to complete it's fighters.
The TEC Percheron Carrier pays about 12 Antimatter for each fighter and has 6 fighters in a wing (again for a total of 72 antimatter). Each Bomber costs 25 antimatter, and there are 5 bombers in a wing (for a total of 125 antimatter). The build time for the fighters is 20 seconds a piece, and 25 seconds for each bomber, resulting in 120 seconds to complete it's fighters and 125 seconds to complete it's bombers.
The Aeria Drone Host takes about 8 Antimatter for each fighter and has 9 fighter wings total (for, once again 72 Antimatter total). The Bombers cost 18 Antimatter a piece and there are 7 of them (for a total of 126 Antimatter, the same as Vasari, one more than TEC). With a build time of 15 seconds for each fighter and 18 seconds for each bomber, it takes 135 seconds to construct it's fighters and and 126 seconds to complete it's bombers.
Interesting how the Antimatter costs are virtually identical, but the build times vary pretty dramatically (although there is around a one second margin of error for the build times and about 1 antimatter margin of error for the antimatter costs for each craft). Each carrier pays "up front" for the antimatter of each individual craft before it's built, so the entire antimatter cost of the wing is not required for the construction to start.
The Carrier Capitals don't appear to incur any antimatter cost for the production of their ships, though.
There are more stats out there for each of the various craft (Vasari have more hitpoints, armor and damage, Advent have the least and TEC has the middle ground) but I don't think they're relevant here. If you play Advent and your enemy is heavy on Carriers, using Disciples with Steal Antimatter can be something worth considering, not so much to hinder your enemy, but since each enemy carrier has a significant antimatter store (TEC and Vasari have 200, Advent have 225) you can gain significant amounts of antimatter off of them easily.
I took too long to write this post, question was answered.