I haven't gotten to pilot one yet, but from the stats it clearly looks like a support ship. It has the best flux dissipation to weapon mount ratio for large ballistics, therefor it's best suited for laying down constant fire, which makes it well suited for pounding ships that can't hurt it. (ie:smaller ships or ships not targeting it)
IMO the Conquest is a damage support that you fly behind the frontline or poke in with from the sides. Myself I plan on loading one side with Storm Needlers, and the other side with Mjolnir + Hellbore, and then hanging out behind a Paragon that I'll sick on the big targets.
One aspect that no one has mentioned thus far is the armor advantages gained from switching broadside faces. Instead of taking all the heat in the face, you're spreading the damage out over two looong sides
Finally, you should look at the effective health points (EHP) rather than just the given numbers of flux cap and flux:dmg ratio. EHP is how much raw damage something can soak. For the Conquest, its base shield EHP is 14300 (20000/1.4). For the Onslaught, it's 17000. Paragon has a fantastic 41700 base shield EHP, and that's not counting Fortress Shield (250 000 for the curious). Odessey sits comfortably at 18800. And you can do the same for flux dissipation. [EHP regen] = [flux dissipation] / [flux:dmg ratio]. EHP regen for the mentioned ships are, respectively, 860, 600, 2080, and 1250. None of this includes how OP meta affects how many points you have left to spend on flux stats.
Basically what the numbers tell me is that Conquest has a shield that's slightly lower capped than the Onslaught but performs substantially better in a prolonged engagement. HOWEVER, the shield ratio doesn't similarly affect the flux generation of weapons! Not only does the Conquest have a better flux cap, it has twice the dissipation of the Onslaught! Aside from the TPC against large targets, they're both dealing with the same selection of weapons, meaning that their flux translates to damage given the same way. The Onslaught might have more initial potential with it's 5 large weapons pointing in the same direction, but in a prolonged engagement the Conquest is superior in all but hull/armor. Onslaught will quickly max out its flux and thus limit its firepower to its flux dissipation. The Conquest with twice the flux dissipation will be able to deal twice the damage. Onslaught might have the firepower, but it doesn't have the necessary power supply to keep up the fire.
Actually something I hadn't thought of till just now is that you could load one side with anti-fighter/frigate weapons and thus eliminate the need for cruisers to do that for you. Your Conquests would be dual-purposed.
Frankly I can't wait for 0.8. Maybe AI will have improved, making Conquest a potential AI pilot-able ship.