Hello!
So faction identities have changed over time, and a few expansions could add a lot of versatility a faction didn't have before. But here's my take:
Rebels have lots of bulky ships like Y-Wings, B-Wings, the Millennium Falcon, etc. While they do have init 5 & 6 pilots, they have few agile aces that can dodge arcs and play the acey game (see Empire below). There's a general on-brand theme of teamwork, with lots of support abilities in their pilots and upgrades. Other than being a bit short on agile aces, they have a wide variety of ship types, with the B-Wing, Auzituck, T-65, and HWK numbering among my many favorites. Most rebel ships tend toward the burly end, with lots of health and relatively little agility, though that's not always the case. While not as agile as more "acey" aces, Wedge, Thane, and Luke are great pilots to build a fleet around (pick one and choose some allies; all 3 could work together too, I suspect, except against a really strong aces player or swarm). A diverse and fun faction to choose unless aces are your favorite play style.
Empire loves swarms and aces. They have lots of fast & agile ships that can either be flown in swarms (TIE Fighters being the iconic example), or operate alone as a "dodge the arcs not the attacks" ace (e.g. Darth Vader, Soontir Fel, etc). Lots of choices of expensive or cheap aces, and this is often the faction of choice for that, though others can do it too. Empire ideally has a theme of most pilots being expendable, hence the Ruthless card, but they don't necessarily deliver on this better than other factions. They also have a theme of professionalism, with support crew and strong pilots coming from lots of training. Very few of their ships are particularly burly, instead relying on mobility and/or numbers. They have very limited options for turreted ships (Decimator and TIE Aggressor).
Scum is a mix of mercenaries (including bounty hunters like Boba Fett), pirates, and neutral groups (e.g. Protectorate). Thematically they also span the timeline, since there's always been illegal and/or neutral factions throughout the prequel, OT, and sequel timespans. Scum's tactics include ships/pilots that operate well on their own (e.g. Boba Fett), bulky swarms (e.g. mixed Kimogila + Kihraxz swarm), and lots of shenanigans like tractoring targets (before the Nantex came along and messed up tractoring rules, Scum were the experts of the tactic). There's less cooperation in the faction than in, say, rebel and empire, and they have very limited access to Force (Asajj pilot and Maul crew, if I remember right, are the only ones). It's a wide mix of ruthless efficiency, daring-do, dirty tactics, and clever shenanigans, but it's also possible to run them in a host of other ways. It's a very varied faction. For an example of how oddball and versatile the faction can be, I point you to the majestic Quadrijet, the lumbering wide-arced YV-666, the quirky Starviper, and the razor-sharp effectiveness of Fang Fighters and Firespray. This faction is also kind of my favorite, though it's really hard to commit to a favorite (I'm one of the crazies who play every faction to some degree).
If you want wide variety, Scum's absolutely a good choice.
Resistance is like a thicker Rebellion (they tend to have a bit more health), but with a more narrow set of options since they're a smaller faction. They also have real, actual aces for their A-Wings (Rebel A-Wings were too fidgety to really fly masterfully; it took the RZ-2 to really bring out the pilots' talent and get to Initiative 5), so they do the ace game better than the Rebels can. Like the rebel's T-65, the T-70 is a basic generalist ship with lots of neat pilot abilities and it's a good core to build a fleet around (IMO the T-70 overall has more interesting pilots). Their resistance transport is a great support craft. They don't have a ton of Force access (Rey pilot & gunner, Leia crew) but that Leia crew is quite good. Between them and Rebels I suppose I prefer rebels just for the wide versatility of their faction. But each can do different things better than the other.
First Order loves its aces. It also has swarm capacity, though not as cheaply as Empire (preferring a shield on their TIE Fighters). Save for the SF Ties they don't do turrets and the SFs cannot fire sideways, but what the SFs can do is pretty cool. They have support through the Upsilon or Xi shuttles. IMO the TIE/ba, TIE/sf, and TIE/vn are great ace choices and you can build fun fleets with any mix of them, or by pairing one or two aces with a mini-swarm. You can also do stuff like 5x TIE/SF with Cluster/Concussion Missiles + Passive Sensors, which is surprisingly effective. My current favorite FO list is Major Vonreg + Kylo Ren (TIE/vn) + Quickdraw, but I haven't yet gotten to explore fleets with Xi shuttles (the Xi added a lot of support options).
Republic is a great place to go if you love the Force, as they have a ton of Jedi. They also have lots of aces. Other options give them a similar style to the Rebellion, as they share a couple ships (or ships' cousins) with the rebels, the Y-Wing and ARC-170. They can swarm with Torrents and V-Wings. They can carry support crew and pilot abilities through the LAAT, but even their aces carry useful team abilities (like Obi-Wan). Right now they're mainly used for their aces, since aces are a very strong playstyle when played right, and aces with force can be very effective. But flying a couple ARCs with a Torrent swarm is good fun, and there's lots of other mixed fleets they do well.
Separatists are very like Scum in that they have lots of neat shenanigans at play. Where they differ though is the massive focus on synergy among their droids. They also throw in some aces through the Nantex, Firespray, and (somewhat) General Grevous (he lacks the init to go toe-to-toe with other aces, but otherwise he shines well). And they have the Force in decent amounts for their faction size. Add the Firespray just because theme, and they have a powerful, scum-like bounty hunter ship. The Nantex is a crazy shenanigan ship, and indeed is potentially a NPE (negative play experience) for the opponent because it can be so powerful and so hard to deal with. I'm personally tired of fighting against Nantex swarms and Vulture swarms; they've been the popular go-to use for the faction because they're just so good. But the Hyena delights me to no end, and there's neat stuff happening with the Sith Infiltrator, Firespray, etc, so you don't have to fly classic vulture/nantex swarms. And if you do like swarms, this faction does those quite well. As with other factions, despite being small, this faction can cover a lot of play styles.
It's very much down to how you like to play, but most factions can do most playstyles to come capacity. If there's a few ships in a faction that just excite you, that's a good reason to explore the faction further.