Edit(This is my loose take on Take on Total War: Disharmony, would be interested to see more fleshed out factions, and those not mentioned)
Alright then... Somewhat unorganized but 'ere we go.
Equestria: Start as either of two Legendary Lords, the Heavenly Twins. Faction wide the units are still broken up according to race (mixed unit being a late game thing, if ever, both due to difficulty in coding it and due to the fact that Equestrians are xenophobes even into the "modern" era) and are typically focused on their interplay rather than using one branch over the others. Unicorns provide basic ranged firepower, with specialized variants giving different affects (basic: arcane shot OR shields, advanced: AOE effects from fire or ice, debuffs, altering terrain, or "summoning" chaff). Pegasi are your cavalry equivalents and are predominantly shock cavalry lacking in staying power with a side order of missile cav for skirmishing. Earths are the typical line infantry, using formations and with a definite bias towards spears and pikes (looking kind of like lances, I guess, strapped to their sides so that only one leg is needed to thrust and pull their weapon).
Of course, the two Legendary Lords need different focuses, don't they?
The basic difference is that Luna is the duelist/militant Lord while Celestia is the political/economic Lord (which forms the core of how the canon timeline could be made from this era, with Luna continuously crusading and finding that gratitude is a very fleeting thing compared to who takes the credit for standard of living increases- skippingallthatloreyoudon'tcareabout!). Militarily this results in Luna relying on a core of professional forces that is fanatically loyal to her personally while Celestia uses levy type units backed by the magical might of the "civilized" portions of the country.
On the battlefield Celestia buffs and heals her side while Luna debuffs and damages the enemy, with that bias weakly transferring to their Unicorn Choir casters and Lesser Lords.
And then there are National traits. Due to how the nascent Equestria works, the three Tribes need to be played off of each other as they still see each other as "Others". Game wise this would be the same system as Maretonia would use with it's Noble Houses, just on a lesser scale.
Sombra: The Dark Archmagus Sombra... Well, he's the Dark Magic faction (well, outside of possible Zebrica alt-starts). Hordes of expendable chaff to bog down the enemy while you bring heavy units to bear on the critical points of the enemy battle line. Few if any subordinate casters mean that Sombra truly is a keystone target, and due to that this faction would not take land in the conventional sense, merely sacking settlements for more chaff, slaves, and money.
Not much nuance to be had here, unfortunately. Just don't lose your (well fortified and defended) capital or You Lose.
Neighpon: Here though, we have some good opportunities for alternative mechanics to make the nation feel unique. Specifically, War Exhaustion. Neighpon does not have a large population, and that means losses on the fields of battle are going to be sorely felt at home. Spending stacks to take territory (in an offensive war, defensively you can probably get away with it to retake core provinces on your island) is a bad idea due to slow and/or expensive replenishment and the public order penalties that will accrue.
As such this is a very "micro" faction as your units have a multitude of special abilities to augment their fighting potential and misdirect the enemy.
Zebrica: Not so much a nation as a mess of alt-starts that share a race, I'd say. The playable Legendary Lords would naturally be the most powerful of them, and as you eat your neighboring Local Powers you gain some of their expertise in their specialty.
Libertalia: As a nation of
pirates, this is more a "for the lulz" nation as a significant portion of your recruiting is either mercenaries from the Great Powers, or actually stealing their stuff either off the battlefield or from their training buildings when you sack the city they are in. Also as a nation of pirates, you do not declare war on nations in order to raid them, while they do need to declare on you in order to invade.
As a marine army, they get bonuses and abilities from staying near their ships be it bombardment, stealth due to weather manipulation, or what have you, making them a poor choice for world domination runs even with getting potential access to everyone's units.
Canterbury: Due to the possibilities raised in thread I can not actually say what they will definitively play like. From the outside they use a hi-lo mix of levies and Knights backed by powerful Caster Lords.
Maretonia: Internal instability personified as they take mechanics from Sombra (slaves) and Equestria (internal politics). The Houses likely play as tight vassals rather than parts of your nation, meaning you have to ask for their household troops and tithes while rewarding them for such via the spoils of the use of said assets.
Militarily they are similar to Equestrian forces, although with a more distinct hi-lo mix between basic mercenaries, good mercenaries and semi-professional House troops, and the Royal Guard and College units/Lords.
Yaks: Smashed between many more powerful nations this nation will have to pick a path to travel, as allies to resurgent Griffonia, mysterious Canterbury, or any of their other neighbors.
Minotaurs: Traders and sailors, the city states are more economical than militant with war typically being a tool of diplomacy over conquest.
Militarily, they are basically the Greeks. Hoplites in phalanxes, archers and slingers, triremes, and so on with the conceit that their Gods are tangible things that can give bonuses for following their Concepts, making for a well rounded empire with many possible play styles. Maybe they can turn to a more militant, Roman type empire with effort.
Changelings: Definitely a !FUN! empire to play, as their style focuses around meddling with the relations of other empires from your hidden crevices while fleshcrafting your troops and Lords into specialized clades rather than training a single body form to do different things.