I would consider Paragon inefficient if it does not have lances and HVDs because it costs 60 DP and moves too slowly (which means already cowardly enemies avoid it if not tied down by someone else, unless they can swarm and kill Paragon easily). Even with ATC, Paragon's range with 700 range weapons is inferior to Onslaught or Conquest with ITU and 900 range ballistics. Paragon with lots of combat skills, a good loadout, and player's willingness to abuse exploits is probably the best at soloing fleets, but it is not good enough to solo the simulator.
Odyssey is a suicidal glass cannon under AI control. AI thinks it is a tank and plasma burns into a mob like Onslaught (and does not try to outmaneuver enemy capitals), but dies too quickly without adequate defenses. It is decent under player control and good against the endgame enemies that matter, namely pirates and pathers.
For a simple bruiser, either Onslaught or Conquest is fine, and more efficient than Paragon that lacks proper weapons. At 40 DP, player can support their non-Paragon capital with a Mora or Heron. Paragon is not quite 60 DP material without beams and HVDs. Against the biggest enemies, 200 DP (40% of 500) is not much, let alone 120 DP (40% of 300).
Onslaught's main advantage is it can be equipped with Open Market junk and still wreck fleets.
Conquest needs some of the rarer weapons and hullmods to do well.
@ Wyvern: While efficiency is a consideration, Onslaught and Paragon have enough OP to afford Augmented Engines. Odyssey does not, and while Conquest might, the sacrifice will hurt. However, Onslaught is a fuel hog, and Paragon is a DP hog. Conquest is one of the more campaign efficient capitals.