Other than tanking damage, and providing a bit of anti-strikecraft duty, the Kol's regular weapons are weak and dispersed in all directions. Its Gauss Rail Gun is total weaksauce compared to the Marza Dreadnought's Radiation Bomb as well. A level 3 Radiation Bomb deals less initial damage to a target, but then deals 210 damage over 10 seconds to all targets in the area. If you're facing 30 ships, that is 6,300 damage applied to a bunch of targets. Those same targets are also susceptible to Missile Barrage once the ship hits level 6. Meanwhile the Kol's Rail Gun zaps its entire antimatter reserves in 15 seconds, dealing a third of the listed damage since shield mitigation deflects the rest. While the Marza scales to meet the enemy threat, the Kol does not. If it were up to me, I'd triple the damage output of its forward beam weapons(maybe even quadruple it). That would put it more in line with the Marza's regular missile volleys, and make the Beam upgrade worth more for the TEC, especially considering it is tier 3 and 4. It would also make the Kol a mirror opposite of the Marza, having it specialize in anti-capital warfare.
All that said, there are ways to maximize on the Kol in the mid- to late-game. The Dunov's Flux Field comes to mind. 60 seconds with -75% antimatter cost means the Kol can fire 12 shots of its Gauss Rail Gun in rapid succession, as well as 6 blasts of Flak Burst, along with its shielding. The TEC antimatter regen buff within their own culture helps a good deal too. For that matter, a starbase with Docking Booms provides similar support. Finally, Finest Hour gives its weapons 60 splash damage to nearby enemies. That helps it propagate damage in combat.
It is just that, as a starting capital ship, the Kol is rather wanting. In terms of raw combat prowess in the early game, a Sova Carrier goes much farther.