After playing as all three races repeatedly, I have been unable to define one ship that I can say is definitely the best.
The Kol is more than capable of facing off with multiple enemies. Its rear firing weapons and ability to broadside targets makes it far more devastating than the others when it is surrounded. Combined with Finest Hour and Adaptive Forcefield, it nearly becomes invulnerable and completely neutralizes phase missiles. They have enough health to be thrown straight into the fray and just a couple of these at level six can easily act as a force to delay an opponent before the rest of your fleet arrives.
The Radiance has very high DPS and carries the most powerful weapon in the game against a single target. It carries Cleansing Brilliance. 2000 damage to the target and when used with Malice, those around it receive 700 damage. It also has Detonate AM which is very effective against other capitals. It also carries Energy Absorptive Armor. This increases armor and regenerates AM.
Last, there is the Kortul. It is able to deactivate fighters from across the gravity well while destroying AM whenever it attacks an enemy. Most Importantly, it has Power Surge. Power Surge GREATLY reduces your cooldowns and thus, the pulse beams deal 150 damage when they would normally deal 75. At level ten, each battery can deal 200 per volley. Not only that, but Shield regeneration is increased to more than four times. Either buff would be enough, but together, they make this ship far more powerful than any other capital ship on the game. Next, it has Volatile Nanites. Nothing kills a fleet of frigates faster than this. It increases the damage they receive significantly and damage nearby enemies upon their death.
Each one has its own benefits. The Kol has defense. The Radiance has Cleansing Brilliance. The Kortul has sheer power. Each is powerful and the existence thereof can effect the outcome of a battle, but I am unable to determine which is the most powerful.