Both sub-factions share all the ships and abilities from Sins, plus a new capital ship that launches pods full of marines to board and capture other ships or destroy them from within -- but the Loyalists get major defensive advantages. The can build multiple starbases in the same gravity well, build the Novalith superweapon early, and their capital ships automatically gain experience when in their own territory, incentivizing players to keep them close to home. The TEC Loyalist Titan, the Ankylon, is a massive tank and buff machine, capable of defending an entire grav well. It can extend its shields around other ships, reduce allies' ability cooldown timers, and extend enemy ability cooldowns, all while giving and taking a severe beating.

And They're Not Gonna Take it Anymore
The TEC Rebel faction, meanwhile, is all about offense. They're rewarded with cold hard cash and morale boosts by bombing enemy planets. They have research unlocks that allow them to first befriend the defending militia forces guarding habitable planets, and then to ally with the Pirates (which will be present even in games where pirate raids are disabled). The Pirates won't attack those Rebels no matter how much bounty is on their heads, and a Rebel player can even stash valuable ships smack in the middle of the Pirate base for safekeeping. As a bonus, the Pirates will contribute ships to the Rebel fleet, complete with amusingly tongue-in-cheek pirate voices. The more aggressive Titan is bristling with weaponry, including an area-of-effect shotgun attack and an Overcharge ability that makes weapons even more potent.
More briefly, Fraser touched on the Advent and Vasari factions. The Advent Loyalists are on a vengeful rampage and use their psychic abilities to their fullest to assimilate enemy ships. Their planets automatically spread culture without the need to build structures, and their Titan can mind-control an entire planet, permanently taking it over. The Advent Rebels, who suspect that their collective consciousness has been corrupted, have the ability to resurrect destroyed enemy ships as their own, and their Titan can consume other friendly ships to keep itself alive.

Finally, the Vasari: the hyper-aggressive Loyalists can no longer sit still and wait for the still-unnamed threat that chased them into TEC space to catch up with them, so they're focused on mobility. They can upgrade their capital ships to produce money, supply, and research, and their Titan can function as a mobile capital world (and also summon Dark Fleet ships). Once they have that, they have no more need for planets, so they can strip them of every shred of resources and leave behind nothing but a dead, uninhabitable asteroid. They're the only faction that's able to keep on fighting with no colonized planets at all. Frazer says it's a risky strategy, though -- you have to be on strong economic footing to successfully pull up your roots, so you can't do it too early.
On the Move
The Rebels, conversely, are willing to play nicely with others. We know the least about them, but we do know that they can allow their allies to use their Phase Gate network (which lets them jump between any two planets).