Vasari to my understanding, they are aggressors with a relatively poor economy, and culture spread (so no TEC credits and no super money making advent allegiance bonuses from culture.) They have resource extraction techs roled into one, so upping crystal and metal income through research is more viable.
NO1 coolest thing to my mind are PHASE MISSILES, as you research Vasari missiles become increasingly likely to negate shields and shield mitigation, so pew pew 
By late game, they can see all phase jumps that occur and can build phase satbiliser networks on their planets allowing you to jump directly between them. So all of your planets in a system are 1 jump away. The Kostura cannon extends upon this, see below.
Finally they get Long range missile shipss with only 1 millitary lab, increasing the speed with which you can turn out vasari pewpew.
Ok superweapon breakdown:
Deliverance Engine (Advent): Target planet generates your culture unstopably for quite along time+your ships hit by this receive a damage buff= this weapon is not for stealing planets, it supports your fleet by buffing your ships and ensuring that major engagements are in your own culture, this gives you culture buffs (advent is bonus shield mitigation) and denies the enemy their culture buff. This is a very usefull super weapon if you shoot the grav well where a decisive battle is occuring, it will drastically increase your chance of victory. Technically it can steal planets, but thats not really what culture is for or good at.
Kostura cannon (Vasari) Target grav well becomes a phase node for a while+ enemy ships are dealt light damage and disabled for 20 seconds+ structures (that means you repair bay) are shut down for several minutes= pretty good also. You can jump from any phase satbilizer in the system to the target planet, where you will find all ships have taken some warmup damage for the ensuing fight and all structures are not capable of taking part. Even just using the phase node opening power this thing is great for outflanking the enemy.
Novalith (TEC): kills population+ damages (3000?) + pop cap reduction for a while+anti colonization radiation for a bit if planet killed= This only hurts planets, not fleets and as a result is kinda teh suck.
These are Entrenchment specs.
