And how do you handle Vasari players? Are they beatable, or fun to play against as non-Vasari? How do you beat them?
If you assume that all 3 race players know what they are doing and no feed is present.
Early game: TEC => Advent > Vasari
TEC: Perhaps TEC have slight advantage over advent but that is because of their cheap tier 2 weapon hull armour upgrades. Without that they would be pretty even.
Advent: Advent are like zerg with cheap and fast building ships.
Vasari: What helps vasari tremendously in first 10 min of the game are neutrals. Without them Vasari are sitting ducks and are forced to play defensively and invest heavily into star bases. Without any good choke points they are as good as dead or locked into HW and hoping their titan will save them.
Middle game: TEC > Advent => Vasari
TEC: Tec is first but only if they if they can get big enough economy to out spam their opponents.
Advent: Advent is starting to invest in their battle ball
Vasari: Vasari has now heavily invested in their phase missiles research which can cause massive problems to advent but only if they have fleet to support them
Late game: Vasari => Advent >> TEC
Vasari: Vasari is king. If they have kosutra game is pretty much over if not once maw bug will be fixed advent (especially loyal) have serious chance to win the game.
Advent: If advent have economy to build 3 Deliverance engines and as long as vasari have no kosutra they won the game. Only thing that could save anyone is vasari mobility trough phase gates with their hit and run tactic.
TEC: TEC especially loyal unless they massed novalith cannons have no chance here. Another way they can win is to have much bigger eco than enemy and are able to field bigger fleets a lot quicker. Most of the time they are just observers.
Disclaimer: Those are only opinions of certain Greg30007