Was wondering which system you'd use to run a game based on this concept?

Edge of the Empire sounds the best version from what I've seen so far but have you been inspired to run games on any of the episodes released so far?

On what concept? It would help if you extrapolated a bit more then the name

Edge of the Empire is probably best. They all seem to have Obligations rather than Duties. The Force characters are the minority, so it's not, in my opinion, a FnD game. I've only seen the first episode though. It's cute.

Do you mean the LEGO Star Wars: The Freemaker Adventures? If yes, then I'd say, based on wikipedia description that Edge of the Empire would be best. And no, I haven't watched Freemaker adventures. Everything I know about it, is based on following wikipedia quote.

The series is set between the events of The Empire Strikes Back and Return of the Jedi. The general premise is described as follows: Told in the whimsically-charged style that audiences have come to expect from LEGO Star Wars entertainment, the series stars the Freemakers, a family of scavengers who build and sell starships from the scoured debris of space battles strewn throughout the galaxy. When their youngest discovers a natural connection with the Force through an ancient artifact—the Kyber Saber—his world is turned upside down, and he and his family are thrown into an epic struggle against the Empire to restore peace and freedom to the galaxy. Throughout their adventures, the Freemakers explore new worlds, meet new and familiar characters, and learn the true value of what it means to be a family.

Just watched the 4th episode and yes I really should have explained myself properly!

Enjoying it so far and can see the stories working in a game just not too sure which would work best even if its clear to others what works the best!

Pretty awesome to see The Wheel on screen, even though it's a bit different visually from prior depictions. Interesting also to see the Trando slave operation on Kashyyyk.

(Yes, I am aware that none of it is canon - but they are drawing on a lot of interesting material. Although I'm not a fan of the Cyber saber concept, but it's a laugh).

I'm wondering if this was where the Sith got the idea for using Kyber Crystals in their superweapons!