The Vasari pack quite a punch with their ships, and with a certain level 6 capital ship, they can open a phase gate anywhere on the map. That ship has an ability that increases speed and makes it jump interference immune, so you can pretty easily get it past defenses to the homeworld, make the temp phase gate and jump your fleet in from elsewhere on the map. Then after they're done, just make the phase gate again and jump them out.

The capital capable of that is the Antorak Marauder. Beat weak in direct firepower, but very good utility. In addition to those two abilities, it can spy on planets and sabotage their construction speeds at the same time, and also phase out other ships to make them unable to do anything but also invulnerable. Good for both protecting your own capitals, and keeping key enemy capitals out of the fight

I play Vasari a lot and I rarely ever use the Marauder but I agree Vasari is probably your best bet for that kind of style mainly because of their mobility around their own territory, with a little bit of scouting you can see where to hit and get there fast with your fleets.  and as long as you don't attack too far in to enemy territory you are never too many jumps away from defending with your attacking fleet when you have phase gate tech up.

Radiance can disable abilities... but not phase jump. I think you're talking about the Revelation Battlecruiser.

Vasari is best for hit-and-run tactics and "fighting dirty". Advent is supposedly best for slug-it-out battles. TEC is best for wars of attrition.

I personally find the Vasari the best for slugging it out against huge fleets because of the carrier cap's Repair Cloud which, although seemingly mediocre, is actually quite powerful. You dont need to split your fleet into offense and defense fleets since phase gates mean you can get to anywhere fast from anywhere, so oyu can commit more ships to a battle. And while Advent might have more firepower per ship (Crusaders are amazing), Vasari can use Subverters to shut huge groups down. If you micro them well you can keep them out of the fight indefinitely.

Vasari are like modern generals. They focus on minimising casualties first and dealing damage second.

Advent are like boxers. Very strong and focus on dealing damage first and healing second.

TEC are like those 12 year olds in Counter-Strike. Not good at staying alive or killing enemies, but no matter how many you kill they just keep coming.