Kortul is quite tough, has an excellent ability (the cooldown one) and can take a lot of beating too. Sadly it's somehow inferior to KOL and Radiance, you don't want to send it one on one.
The Kortul Devastator doesn't do well in straight fights against the Kol and Radiance because:
1. It doesn't have the immense armory and hull strength of the Kol nor the immense shielding of the Radiance, but is instead somewhere in between.
2. It's firepower comes more from research than leveling up, since it's Pulse Beams get a whopping 35% damage boost and it's Phase Missiles get 25% shield negation and 20% damage boosts from research. Most of this firepower is also concentrated on it's side banks or is manifested through it's bomber squadrons(75% damage vs. cap-ships), with only the weaker Wave Cannons being completely front-facing.
3. The 2 battleships have abilities that look as if they were designed to screw the Kortul. The Kol's Adaptive Forcefields make it a point to nerf Phase Missiles, and the Radiance Battleship's Energy Absorptive Armor completely neutralizes Disruptive Strikes in the most precise and perfect manner. The Radiance's Detonate Antimatter, and the Kol's Gauss Railgun and Finest Hour abilities are specifically anti-capital ship while Power Surge and Volatile Nanites are support abilities which help fight off fleets of frigates or cruisers.
The Kortul is more of a mixed-fleet combat-support capital ship with heavy weaponry and defensive features designed to make it fare better when faced with heavy cruisers, bombers, LRFs, etc., but not other battleships, unlike the Kol and Radiance which are of a more anti-capital nature.
The Skirantra and Antorak are also very nice with their abilities that make them more optimized for long-range fast-strike carrier fleets in different ways. The Skirantra with it's Repair Cloud and Microphasing Aura make friendly strike craft more durable in battle, but the Antorak is still better for supporting a carrier fleet since it's direct firepower, Distort Gravity, Phase Out Hull and Stabilize Phase Space abilities all add to the speed and disruption capabilities required to shepherd carriers away from danger and take out flak without engaging the actual enemy fleet, and therefore allowing strike craft to deal tons of damage to their hapless targets.