I've actually spent a decent amount of time thinking about this kind of thing. Here's my thoughts.

Rebels: The formation faction. In movies, rebel ships all fly in formation, have formation-based call signs, and sacrifice themselves so the one guy in the formation can shoot his torpedo into the Death Star. In the game, Rebels tend to get rewarded for keeping in formation. A lot of their abilities trigger in the engagement phase.

Resistance: Every time you see these guys fly in formation in the movies, they start blowing up and fail. This faction doesn't have abilities that reward them for formation flight, and they seem to prefer flying on their own and having enemies in various arcs (bullseye, turret, front, etc). Their abilities also lean towards movement, and are usually more "active" in the activation phase than the engagement phase.

Republic: The clones of the faction tend to be rewarded for staying in formation, but the Jedi don't particularly care. They seem to be a mix of the Rebels and Resistance to me. A bit of self-sacrifice (Dedicated vs Selfless), a bit of flying on their own to get people in bullseye arcs.

Imperial: The faction that punishes their opponent for taking damage. Maarik, Zertik, Del Meeko, Gideon. They also get a lot of extra movement options to move quickly (Gunboat, Reaper, Striker, Interceptor linked actions) which they use to get shots off from unexpected directions.

First Order: The faction that punishes their opponent for dealing damage. Fanatical, Quickdraw, Tavson. They get a decent amount of "attacking from unexpected directions" as well, with Silencer movement, FO's super blue dial, and SF's alternate arc missiles. You can see how they evolved from Imperials.

Separatists: A bunch of drones protecting a queen. The separatist lists that I see being popular are going to be a Solitary Droid carrier with a flock of easy-to-kill pawns. Do you go after the queen piece buffing all the pawns, or just clear out pawns ASAP?

Scum: The range 1 faction: Boba Fett, quadjumpers, Fang fighters, 4-LOM, Guri, Fearless. This faction likes having enemies close up. Also, they have a lot of control token access: tractor, jam, ion as a minor theme. Finally, asteroids are another minor theme: Tobias, Qi'ra, Mining Guild.