I don't think anyone has tested all of the Capitals, but it just so greatly depends on the experience level and abilities chosen (even Level 1 abilities can sway battles). A Radiance with Animosity won't be that great a threat, but put that into Detonate Antimatter and suddenly it's dealing more damage and preventing whatever damage the enemy has from it's special abilities from coming to it. From what I've seen, the Radiance and the Kol seem to be the best Capital sluggers.
The Radiance can employ Detonate Antimatter in a 1 vs 1 fight, which damages the enemy Capital, drains antimatter, and disable it's abilities, all of which are great in a 1 vs 1 fight. Energy Absorptive Armor allows the Radiance to improve on the Advent's traditional weakpoint, their low armor levels (as well as gain some antimatter from being attacked). Animosity has no effect on 1 vs 1 battles. Cleansing Brilliance, at least on paper, looks very good, but it is affected by shield mitigation, and because it is not a single burst of damage (250 damage a second, for 8 seconds) the target tends to max out it's mitigation before ability is even done firing, resulting in the target often taking much less damage than it should. Cleansing Brilliance is awesome against a clustered fleet, but on a 1 vs 1 fight with mitigation and it's long cool-down, it isn't that great an asset.
The Kol can have the Gauss Rail Gun, which like Cleansing Brilliance is affected by Shield Mitigation. However, due to the very short cool down and decent damage at level 3 (some 800 before mitigation) the Gauss has the potential to do much more damage to a single target in a set period than Cleansing Brilliance, assuming the Kol has the Antimatter to do so. Adaptive Forcefield is more effective than Energy Absorptive Armor, but unlike Energy Absorptive Armor isn't passive, at high levels it can be simply chained constantly, but it does drain antimatter for each use. Flak burst would have little substantive impact on a 1 vs 1 fight, except if they both were at higher levels and deploying bombers. If it's a high level fight and the Kol has Finest Hour, that ability alone gives a substantial boost to the Kol's survivability, since Kol's with that just become very hard to kill and even harder hitting. I have no idea if Detonate Antimatter can get in the way of Finest Hour once it is cast, though.
Most of this is just "on paper" and in theory. I've never had Capitals alone slug it out without support of some kind also in the battle, and testing with an AI is impossible. If anyone would like to get on ICO and test the level 1 Capitals, 1 vs 1 with various abilities (which I expect would be very time consuming) just say so, I love this stuff...