This is meant as constructive criticism but will probably just come off as complaining, so to clarify the motivations behind some of these thoughts: I like reasons in games - I want to know why events are happening, and why I should do something beyond 'here's a quest/enemy to kill/place to go.'
I don't really feel that anything like that comes across with the Advent factions.
The Other Factions
The TEC and Vasari are pretty clear.
Gameplaywise the difference is obvious: offence verses defence.
Likewise the story is more-or-less clear, and we can even extrapolate a little more. The rebels are likely mostly the younger citizens and the frontline worlds, those who have only known war and/or borne the brunt of the war. The loyalists are probably predominantly the older military personnel and the scions of the powerful trading families - those who either remember or have been brought up to believe in the prosperity of the old days and want to recreate them behind their ring of steel whilst the enemy exhaust themselves against their defences.
Then the Vasari:
Again, gameplay is pretty clear-cut, split between those who dig in and those who strip planets to bare rock in the later stages of the game (though obviously I have no hands-on experience to truely judge).
Storywise it's pretty easy to imagine where the split arose - besides giving up, there are only two mindsets that will realistically develop within a culture like the Vasari Fleet, you either resolve to end it somehow (and the martial prowess of the TEC and Advent might be enough to win such a fight) or you become so accustomed to running that's all you know how to do. The conservative Vasari want to run, since that's always worked before. The others are tired of running, maybe even have hopes of restoring a New Vasari Empire once the unseen threat is defeated.
But I don't really get anything like that from the Advent.
The loyalists are pretty much the Advent we know and love/fear: fanatics bent on forcibly converting or killing any heathens they come across to avenge their forebears and their lost homeworld.
The rebels are, erm... fanatics bent on destroying their enemies and... slaughtering their own people.
What diferences there are aren't very pronounced, and in some cases don't even make terribly much sense.
For a start, the split is vague - the rebels think something has corrupted the Unity, the loyalists want to continue the crusade. We can still infer some things from that, though. Namely the rebels have done some soul-searching, there's even some suggestion they'd rather reach out to the enemy than spend more resources and lives on a war they think they may have been 'tricked' into.
In terms of a story there's not much there, but in-game the abilities and research doesn't really seem consistent with what little we do have. If anything, the rebels seem more aggressive (like the TEC rebels).
And, to get back to my obsession with reasons for doing things, I find it odd that a lot of their abilities seem geared towards killing themselves and their own people. Admittedly, this is because I expect them to be more introspective and philosophical, but I think that's a fair supposition: afterall they have questioned the divine will of the Unity and forged their own, they would probably be more cautious in thinking they are totally, infallibly right. I'll return to abilities a little later, though.
My (Halfbaked) Alternative Suggestion
We (well, I) need a bit more of a storyline or narrative. There's even one suggested in the choice of portraits on the faction selection screen. The loyalists is a portrait of the woman who often appears in connection with the Advent (as you would expect of the loyalists), who is most likely a Cerebri. The rebels is of the masked individual (possibly male, hard to tell though) in something like a flight suit and sealed technological helmet that I've always thought of as an Anima (the helmet and its antenna just look like something you would wear if you were controling a squadron of drones from a host ship).
To me this is quite suggestive, since perhaps the caste system within the Advent has something to do with the split within the Unity. The more facility with the Unity you have the more power and respect you get within Advent society, and closer you feel to (and more power you have within) the collective network of the Unity itself. However, I recall from somewhere that the Anima get a good deal of respect based on their posession of telekinetic powers with which they can control the drones, but are also feared a little by the higher ranks since their power is more physical and destructive than the nuanced mental abilities that improve interaction and immersion with the Unity (on which the power of the Cerebri is based). Even without the enhancements and extensions provided by their ships' systems they could still crush a person into the floor.
So, maybe the split arose along predominantly (but not solely) caste lines, with prominent members of lower, less-integrated castes or groups becoming disatisfied with the loss of life ('The Unity has fallen silent on one of our worlds!') and resources of the war, whilst the higher castes like (most of) the Cerebri identify more closely with the will of the Unity and the message of a holy war against the TEC.
It would work like this:
The loyalists are the majority of the Cerebri and their followers, those who have most confidence in the Unity and its message. They have a larger stake in seeing its mission brought to fruition and see themselves as the Unity's true followers. They were and are the most fanatical of the Advent, and will conquer or convert any systems they come across. Its will is their will; it is their anchor and guiding star, beyond question.
They should focus more on manipulation (as they seem to already, evidenced by their titan's ultimate). If anything, the loyalists should have things like 'Wail of the sacrificed'; for reasons outlined above, it doesn't seem like something a rebel Advent would contemplate - they've questioned the rightness of the unity, the loyalists on the other hand have unwavering faith in their chosen course of action. Sacrificing one's people and ships would be more in-keeping with a loyalist, fanatical Advent than a rebel who has questioned that fanatical outlook. So long as the Cerebri remain to guide the Advent, no cost is too great in the service of the Unity.
The rebels are largely middle- to lower-ranking individuals in Advent society, those less integrated into the Unity network but still with a stake in it (they're still Advent and still have the psychological and cybernetic connections to it) and thus with an interest in rehabilitating it. The Anima have risen to prominence within the faction, ranking alongside those Cerebri who sided with the rebels, due to their martial prowess and role within the military. Despite this more martial outlook they would rather avoid further unecessary loss of Advent (at least rebel Advent) life and so be a bit more defensive, but in a mobile sense rather than the entrenched defences of the TEC loyalists.
Culturally-appropriate techs would be interesting too - 'Explusion' still fits well, to my mind, since it represents the vidication felt by the rebels as they cast out the invaders: they questioned the Unity and changed their part of it, they were tested and proved themselves still strong. Ability-wise they would focus a bit more on psintegrat and, mainly, telekinetic powers (due to the social and military emphasis on Anima, maybe representing that they've opportunistically grabbed a measure of more freedom to develop their talents now that the Cerebri do not have a monoploy on power). A new idea might be:
An ability that improves Temples of Comunion so that they slightly increase the speed of friendly ships within their gravity well, representing the increased presence of Anima and other telekinetically-gifted individuals being trained/preaching/whatever it is they do there. This would increase fleet response/deployment times within their own borders, without giving an overwhelming advantage in terms of offensive strategy.
The rebel titan's abilities also need overhauling*, and a ship with a large Anima contingent could give some good reasons for some interesting abilities, beyond drone control.
"Embrace Of The Unity": A complex field array works in conjunction with Anima and Psintegrat adepts to pull enemy vessels into the embrace of the Eradica. An AOE attack that reaches beyond range of the titan's weapons and draws enemy ships closer to it, pulling them into range of it's guns (or further in, as the case may be). Used in conjunction with the repulsion ability of the Iconus, could be quite interesting to use to funnel enemy ships into kill zones.
"You Shall Go No Further": The Anima focus their efforts on holding the hulls of enemy ships still. A targeted AOE attack that stops (or slows, depending on how overpowered it seems) a group of enemy ships, most probably just corvettes, frigates and cruisers, not capships. They can't run away/advance on a more vulnerable target, but can still shoot and use abilities (compensating for it being AOE rather than a single ship).
This narrative could even raise some interesting questions about the malign influence that the rebels think has infected the Unity. Are the Cerebri a.) the influence itself, having long ago subverted the will of the Unity and its message to their twisted desire to retake the homeworld and force the TEC to submit; or b.) the main puppets of the influence, being so closely integrated with the Unity they can no longer distinguish between their own will and its collective (and now corrupted) one? For a variety of reasons it seems more entertaining to leave that question open.
I don't know how much these suggestions and (hopefully constructive) criticisms will be. Particuarly as I don't think I've been active since the last beta, for Diplomacy.
But hopefully it'll be food for thought, and if anything maybe underscore the need for some more narrative feedback on why the factions are doing what they're doing. (Descriptions of techs that mentions 'the purified Unity' don't really cut it with me, and if anything just represent the dissociation between the reasons for the split between loyalist and rebel, and the techs these two sides are actually researching.)
*Just generally, also, even if not along these lines. The abilities seem a bit weak, and are also predicated on your fleet dying, rather than any kind of genuine synergy between it and the titan; complaints I've seen made elsewhere. Basically, the first is a bit silly - and is the same reason I don't tend to build the Corsev: too much micro-managing in the occasions when it actually becomes useful; and at least the Corsev can steal ships to use it on rather than ones you've paid for - as well as a waste of resources (for it to be worth using, you need to use it on an undamaged ship to get all those nice hull and shield points, rather than on an already dying ship which nets you very little). Not to mention that, from my point of view, there's the same 'why would rebels sacrifice themselves?' question hanging over it's narrative provenance. The third is passive, but 'I can't do anything fun with it other than move and shoot' isn't really a good criticism, and the second is fairly reasonable. The ultimate, meanwhile, needs you to basically lose the Titan to come into play.
Less said about it's looks the better. That disk is just... inelegant, a word that should not be applied to any Advent ship. Although I thought I could just about get used to a vessel that looks like a cross between Gormley's Angel of the North and the nightmare-moth-creature from Perdido Street Station, the disk I just can't get used to.