Republic-Movement breakers.
Seppies-CEs and powerups for Droids.
Rebels-Great shooters and synergy between their Uniques.
Imperials-Swap+great commanders, especially for non-Uniques.
NR-Hard to say, honestly. Not enough epxerience with them.
Vong-Losing? No, but really, they are pretty strong now. I'd say the CE stealing of the Yammosk is the only thing that could qualify as a Gimmick, aside from near-universal VCA.
Mandos-CEs for Mandos and abilities letting large number of your squad move pre-round. (Resol'nare and Battle Ready).
OR-ABM.
Sith-Good beatsticks and support for them.

Old Republic: ABM is their really big thing. After that, most of their good pieces are force users of some kind.

Sith: Big brawlers is the primary thing they've got. Sometimes they have some neat Force tricks (like Caedus), sometimes they have great CEs (like Revan and Bandon), sometimes they just beat things up (like Maul SI). Mostly expensive pieces, though. They do have a couple of neat options in the 30s point range, but you would usually play at most one of them as a backup character to the big guy.

Mandos: Shootin'! The shootiest faction in the game. They also have a lot of denial abilities, and are good at making your opponent not do what they want to do. Good synergy between their non-uniques, too.

Seps: Droids and Twin Attack. Whorm Loathsome is their main man. They also usually play very high activation squads, partly due to Gha Nachkt being a good bargain in an already droid-heavy squad to bring in 2 point Mouse Droids and then Poggle the Lesser for the 2 point Geonosians.

Republic: Lots and lots of movement breaking, then high-cost Jedi like General Skywalker, Yoda on Kybuck, Mace LotLS, and GOWK.

Imperial: They're the best swappers, with Thrawn being better at it then Panaka (mostly because of his Opportunist CE). Ysalimiri is another thing that they have that others don't. They want to outactivate generally to get that Opportunist off.

Rebels: Cheap CEs and lots of them. Tons of synergy, but very little staying power. Big on door control with the ERC.

New Republic: Some good cheap characters like Rebels, but also some powerful Jedi. Not many strong shooters. Very unique-focused.

Vong: Major melee faction, as well as crab armor on almost everyone, but the biggest thing is probably Force Immunity.

Yeah, Han is good, and Winter can be good enough in the right squad. That's basically it, though.

I agree with you on mostly everything (including the Vong), but I think the gimmick for NR is that it has so many Gimmicks to choose from.

Yeah, that's probably ight. Like having Luke, GH; or Mara, or Kyle+Jan. There are a lot of different bases for a competitive squad.

If only they could get death shots from within the faction.

In other words, and JHC here more expert than me, the Vong don't feel Vong enough. They are Melee centric (success), tough (success with VCA), disposable (success in cheap fodder) and would sacrifice for the greater of their whole (not quite there).
SD 20 is very good but they had a lot of spiteful tricks just in case they were defeated (poisons, toxins, symbiotes, berserker rage, etc)

Just my opinion.