If we're just talking about which one is most cost-effective, as in which one requires the minimum amount of supplies to recover from the CR reduction for deployment, then that would be the Gemini. (Incidentally, the changes listed in the 0.6.2a patch notes will not affect the cost efficiency in this sense.)
You have six options for carriers:
Astral: -30% CR/deployment, +5% restored per day => 6 days to recover at 20 supplies per day => 120 supplies per deployment
Atlas: -15% CR/deployment, +3% restored per day => 5 days to recover at 5 supplies per day => 25 supplies per deployment
Condor: -20% CR/deployment, +10% restored per day => 2 days to recover at 4 supplies per day => 8 supplies per deployment
Gemini: -15% CR/deployment, +8% restored per day => 1.875 days to recover at 2 supplies per day => 3.75 supplies per deployment (probably rounds to 4)
Odyssey: -40% CR/deployment, +5% restored per day => 8 days to recover at 15 supplies per day => 120 supplies per deployment
Venture: -20% CR/deployment, +10% restored per day => 2 days to recover at 8 supplies per day => 16 supplies per deployment
As such, the Gemini is clearly the cheapest carrier to field in terms of the cost of recovering the combat rating. However, there are other factors to consider:
1. Both the Gemini and the Atlas provide large amounts of cargo and fuel capacity relative to the other options in their weight class (Gemini - Condor, Atlas - Astral and Odyssey), but are relatively fragile
2. Crew requirements, in order from least to most: Gemini (35), Atlas (50), Condor (65), Venture (125), Astral (350), Odyssey (400)
3. Whether or not you can use the carrier to replace another ship: Gemini, Condor, and Atlas would only be deployed for the flight deck. Venture is a decent cruiser, Astral is on par with a heavy cruiser, Odyssey is almost equal in a straight fight to either of the two battleships, but not quite.
4. Is it more efficient to use my carrier to fill a secondary role (Venture - cruiser, Odyssey - battleship if there aren't any real battleships around, Gemini/Atlas - fleet tender) or to have dedicated ships? Is it worth risking the secondary aspect of the carrier I choose in fleet actions?
5. Tactical Speed, in order from greatest to least: Gemini and Odyssey (50), Condor and Venture (40), Astral (30), Atlas (25)
6. Maximum Burn, in order from greatest to least: Gemini and Condor (4), Venture and Odyssey (3), Astral and Atlas (2)
7. Deployment points required, in order from least to greatest: Atlas (7), Gemini and Condor (9), Venture (12), Astral (22), Odyssey (25)
8. Where you want the carrier to be in your fleet - can you mount long/medium/short range large/medium/small weapons, which weapon types, how many weapons, and how tough is the ship (shields and hull)? (As it happens, the Venture has as much hull as either the Astral or the Odyssey and better armor, but less efficient shields with a lower flux capacity)
9. How many flight decks do you need to keep your two or three fighter groups in action in a typical battle? (Probably only one.)