Holy crap, my thread got linked to twice! 
A fully upgraded Transcendia gets slightly over 10k shields and about 17.5k hp, which actually puts it right around the Argonev. Having 70% shield mitigation instead of 60% puts it over the top in survivability. It deals about 191/200/148 damage with its 3 weapons by info-card with the lowest being the psi-pewpew. Meteor and Mass Disorient is a fantastic combo, because Disorient makes a ton of ships unable to fire since weapons require facing and disoriented ships just spin around.
Anyway, Adjudicators are great for taking out clustered defenses of the TEC/Vasari, but they're much slower on Advent's (shield mitigation on turrets) and starbases, since they trade high single target damage for being able to attack 5 at once.
I've never had a problem assaulting starbases directly, though it does depend on the number of ships I've got. Guardians + Progenitor's shield restore is still a great combo to use, due to the starbase attacking lots of targets. All starbases are also defenseless against bombers and rely on other things to take 'em out. The TEC hangars aren't that much of a threat when you got enough bombers going since they're still limited to a few targets at a time, but the Vasari ones are annoying since they hold your mass for a while 