So looking at the different specializations there is a serious problem with the different chassis that get used, in that some of them are very powerful and some are not.
The stalker and zealot are fine as is, since they have abilities that function well with their class abilities. Not sneak attack and weak divine spellcasting along with a small boon are perfect starting points for the class.
Avenger and Warlock however are not equal by comparison. Psudo-full BAB and a spellbook are not comparable class features to not sneak attack and a cool divine power. Both these specializations need extra umph at first level to make them not only equal to the other specializations, but to other classes as well.
The social aspects of the class are nice class features, but hardly practical when it comes to the way the class needs to function in order to not die.
I recommend Mystic Bolt be granted to the warlock and signature weapon be granted to the avenger at first level. In the case of the latter, it could probably be worked differently so that it isn't just a couple of fighter feats, but rather an actual special weapon or type of weapon that the vigilante uses, like green arrow's bow, or batmans spiked gauntlets.
Avenger is the primary martial aspect of the specializations, and he sucks hard compared to the stalker. I think Fist of the Avenger and Signature weapon oughta be combined into a single class feature and baked into his assault training. See the warpriest's sacred weapon for this. He gets Weapon Focus for free, and can boost his to hit and damage with a limited resource pool at first level, in addition to spellcasting. We need something like that. Fist of the Avenger should not include a damage boost, but rather allow you to be part monk instead of fighter.
I agree with the, what I call "balance issues", though parallelism does sound better. We may be focusing on the wrong things here. This vigilante system seems to be bringing us one step closer to a backwards compatible Pathfinder system that is classless, and you simply pick your class abilities, HD, BAB, skill points, etc. If you pick something that makes you sub-par, well, you picked it. However, Yes, I didn't like that I could not find a way to get a full BAB build with the Avenger spc, the warpriest mechanic is the perfect fix!