The Advent are vastly more powerful than the other races, but there is no way clear way to balance them. If illums are nerfed then the advent have no strong direct combat units until HCs, it already takes longer to get illums than any other lrf. Their greatest weakness is an early game rush, before they can get enough illums and guardians out.
The idea of a race with many synergies between abilities is great, but when you put it up against two other races with very few ways to counter it you get advent ownage.
Advent ships in general have more shields than they do hull, so you would expect PMs to lay on the hurt, but the vasari ships are so much weaker than advent ones (in general) that it makes little different.
The TEC have a great eco so they should be able to outproduce the Advent and overwhelm them with sheer numbers, but a well balanced advetn fleet can take on a fleet three times larger, with a little micro, without losing a single ship.
They arent overpowered because of one great thing about them, they are just able to nullify the other race's greatest advantages.