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.
The DE is the cultural equivalent of a planet-buster missile (or the Terror Star in GalCiv 2 Ultimate), with the additional advantage of it only killing the enemy's *culture*, not the people. If you have a multi-sided game (either online or offline skirmish), being able to use the DE on the most troublesome side's planets frees up resources to tackle the remaining (if not as troublesome) opposition. However, the Advent have other advantages in smaller maps (where the Deliverance Engine, or other superweapons don't come into play), such as Galactic Rift (inactive pirates).
The Deliverance Engine has another major advantage over the other superweapons; because it's a culture-buster, you gain all the target planet's improvements (and resources) without having to chew up time/metal/crystals/additional cash on a traditional beat-down invasion/re-colonization. (Let's face facts, a traditional invasion chews up resources that can best be used in moving further up the tech or fleet tree, and *all* the superweapons, including the DE, are well up near the end of each race's tree; if you're playing as the Advent and you've reached the Deliverance Engine and *haven't* wiped out all the opposition yet, you're in no position to waste aqdditional resources, or time, continuing down the traditional route to victory.)