When did the Advent start getting a weapons bonus for culture? Last I checked, their culture buff was only an increase in mitigation.
Personally, I much prefer using the Deliverance engine in protracted multi-star games (which is generally the only time I see superweapons used at all unless I'm just screwing with an AI). It hinders the opponent's economy, gives you a good look at their empire (provided you have the appropriate research), supports your fleet, removes culture buffs from theirs, gradually turns planets, and makes it harder for the enemy to take back planets that have been turned. Or, if nothing else, it makes your opponent invest heavily in culture to counter it.
If the goal is simply to win the game as fast and as efficiently as possible with the lowest amount of micromanagement, then yeah. Despite the above benefits, the Novalith is still, most likely, the better choice.
The Kostura sounds good on paper but in my experience, it's just too awkward to be useful. Timing fleet strikes with the stun effect never seems to work out how I'd like, especially in multi-star maps when the shots take an eternity to connect, and the damage never seems to stack properly on multiple shots so using it to harm orbitals isn't terribly effective either. I've tried it a few times and I've been disappointed with the results on every occasion.