This is a straightforward thing to work out, requiring just a tiny bit of math.
Flux dissipation is the most important stat for any ship in this game. (since the higher it is, the more dps you weapons can output or the more shots your shields can tank)
Flux doesn't apply to missile weapons, so I'll include how many slots each gets. You could in fact figure out the dps of a missile weapon slot on average (assuming it's loaded with harpoons and only 50% of the missiles hit or something) and figure out what the equates to in flux (the good weapons in this game tend to add about 1 flux per dps). For some quick math, I'll count a small missile slot as 1 point, a medium as 4, and a large as
10. (since a small harpoon rack has 3 missiles, a harpoon pod has 12, and a hurricane mirv does double the dps of a harpoon. Also, hurricane mirv is more likely to hit through defenses)
Well, if you look at the capital hulls, the flux dissipations are :
Astral-Class 600 bad 2 large 2 small, so 22 points. Costs 20 supplies/day.
Atlas-Class 200 garbage no missiles Costs 5 supplies/day
Conquest-Class 1200 2 large 2 medium, so 28 points. Costs 15 supplies/day
Odyssey-Class 1000 3 medium, so 12 points. Costs 15 supplies/day
Onslaught Class 600 bad 4 medium missiles, so 16 points. Costs 15 supplies/day
Paragon Class 1250 4 small missiles, so 4 points. Costs 20 supplies/day
Prometheus Class 300 garbage no missiles. Costs 5 supplies/day.
Now, it is obvious why the Conquest is the best capital ship. This isn't "personal preferences", it is far superior in current game balance. Note that not only does it get the most missile slots, and the second most flux venting, but it costs less in supplies per day than the paragon. (which has less flux venting as it is)
The Odyssey-class is a distant second, since it does have more dps with energy weapons due to the high energy focus. Energy weapons also get a bonus when the ship's flux is rising, and the bonuses stack. The odyssey also throws in a flight deck, and it takes half the flux for incoming shots. However, it has less ordnance points, so you can't fit as many guns anyway. Also, it costs 50% more supplies to fully repair, and that's a critical problem in the current game.
The paragon isn't worth it - it's slow as a snail, has less dps than the odyssey, bad maneuverability, too many supplies/day, and so on. It might be an ok ship with modded weapons that have more DPS in a large energy slot. The real problem is that it costs 5 more supplies/day, and you could have a conquest and something else instead.
The reason the Astral class is garbage is because you could bring 3 gemini class freighters instead, with 2 tow ships for each, for a total supply cost of 12, instead of 24 for an astral class + 4 tow ships. The freighters are much cheaper to operate.