Alright, lets do this.
The Republic: At its height you could have argued that it was the Roman Republic, But it struggles to leave a lasting impact on.. well anything. The Jedi seemed to mostly moved on to more relevant factions like the GA and SSC. At its height I would say it would be the Second French Republic, in it current state... Kingdom of Soissons, have fun holding out guys.
The One Sith: At its height I would say the Ottoman Empire, there a large faction the conquerors in the name of the Dark Lord (Sultan), and has no uniform Sith ideology. Right now your still the Ottoman Empire, just the one in the 1700s. In terms power projection they need need a win against the GA to be taken seriously. Beating up the pubs doesn't score you any points anymore. They also need to take back the Maguffin.
Galactic Alliance: A faction dedicated to taking the fight to the OS, they may seem like some kind of military order of medieval times. But the lack battles after narrow loss to the OS rules out that kind of comparison. Has an outstanding power projection situation with the OS, in all fairness I dub you guys the European Union. Now show that military can do something.
Mandos: Fill in your choice of native american tribe or Eurasian Khanate of choice here.
First Order: Italian Social Republic, score a big win and you'll get Third Reich.
SSC: Surprisingly versatile in the face of defeat, and remains solid on its map position after a push by the Primeval. I dub thee Crown of Castile (no Inquisition edition).