At first I thought adjudicators were crap, escpecially when comapred to ogrovs. But a Played a 4v4 game the other day on Areolian sector in which our opponents had built 6 or 7 starbases at their star. One of my allies went in with 20+ adjudicators and destroyed most of them while the rest of us battel the opposing fleet at a different star. These weren't weak sbs either. My ally managed to fight off a fleet being produced by the TEC starbases AND destroyed 5 starbases before our opponents surrendered.
That gave me a little more respect for the little starfish shaped craft.
I find though that they are best used against all the tactical structures people may build as stated above. Adjudicators tear through turrets, squadron bays and regen platforms, but they can be used effectively against starbases.
If you're taking on a lone SB, I would recommend using them with a few additional ships like guardians to help defend them against SC and meteors and a couple of drone hosts to add fighter/bomber support. I mean it's either that or build a ludicrous amount of illuminators with the illusion ability, which I've noticed tends to trump everything. In the game mentioned above, one of our opponents had 150+ illums which wasted a half upgraded tec sb in seconds, then quickly doubled in size to take on my 80 enforcers and two other similarly sized allied fleets. We lost the battle but won the war.
BTW, taking on a fully upgraded Argonev with just HCs = bad idea. I found that out the hard way when I sent about 70 (non upgraded) enforcers up against one and retreated with about 13. I had only taken it down about 2/3 when I pulled out. Not trying that one again.