The Engine is meant mainly as a massive support weapon, not a direct planet killer. It can flip planets if you chain enough shots since it has a massive culture spread and lasts a while, and it's easiest to do with the empire's border planets that are below 50% allegiance.
The main shining point of it is that basically you can get your culture bonus (+6% mitigation) anywhere on the map and at the same time deny your enemy his. For example, if you're attacking a Vasari player on his home turf, you can deny him his +15% damage bonus from culture and at the same time directly increase your own fleet's damage reduction. 6% mitigation might not seem like much, but it translates to a considerable damage reduction:
Say you have a ship at 60% and you get shot for 100, you'll take 40. Now with the Engine, you have 66%, so you'll take 34 points, that's 6 less damage or (6/40) = 15% damage reduction, and adding that the enemy fleet does 15% less damage (if Vasari), you get a combined 30% reduction in damage taken. Now Advent's shields typically cap out above 60%, so the actual damage reduction from the Engine will be higher in most cases (going from 70% to 76% mitigation is a 20% damage reduction).
The Kotsura disables all orbital buildings for 3 minutes, all enemy ships for I think 15 or so seconds, and does 10% of their max (not current) hp in damage. It's a great weapon for breaking through those 35 point defensive turtles
