Actually most players of all races tend to use bombers because unlike assault (torpedo) cruisers, carriers can attack numerous other targets efficiently. But the official Vasari starbase counter is... the Vasari starbase. The first weapon upgrade deals antimodule damage, which makes it effective against starbases and other structures. Also, I'm told the frontal shield ability can offer further support. There is also a "cheat" where you order the Vasari starbase to move over the opposing starbase with the Z-axis control button, which allows it to fire down at the opposing starbase without taking damage. However, do not do this on multiplayer, you will have players get pissed at you.

The planet-assault Vasari capship (for the life of me I cannot remember the name right now), the one w/ the missile swarm, is also really good at assaulting starbases. The bonus damage it gets vs structures applies vs star bases, too. Also, the disintegrate ability rapes caps/starbases.

Furthermore, a pair of lev 10 Kortuls can facerape a starbase by themselves given a enough time.

And lastly... the Subverter shield debuff works against star bases... so... that + phase missiles (including bombers) = lol, starbase! You can make it even more hillarious by popping the lev 6 Kortul ability on the starbase (the +30% dmg one). Add the Jarasul's nano disassembler into all of the rest of that... you get the idea.

Be prepared to lose some ships though, unless you use a ton of bombers (alone), or have a couple skirantra's and/or a ton of Overseers repairing your fleet.

-Itharus

 Z axis basically makes it so the other player has to pay attention to what you're doing, a lot of players get really bawly about it.