FFG's Star Wars is one of my favourite RPGs, and I think the proprietary dice get an unfairly bad wrap. It's quite possibly the quintessential neo-trad RPG, blending typical trad elements like attributes, skill list and mechanically detailed gear, with the tiered success common to narrative systems.
You're right about the modular lines. They're split by theme:
Edge of the Empire is the "scum and villainy" line focused on scoundrels, bounty hunters and the like;
Age of Rebellion is the Empire vs Republic/Rebels line focused on soldiers, spies, etc.; and
Force and Destiny is the Force-users.
They're 99% compatible, with the only significant difference being a single mechanic: Obligation/Duty/Morality, respectively. Obligation is essentially a debt for EotE characters; Duty is the reverse for AoR characters; and Morality represents Light side vs Dark for force-users.
The reason for the "funky" dice is because the game uses 2 axis for results: success vs failure, and advantage vs setback. This results in the full gamut of "yes, and" through to "no, but":
Success with advantage = yes, and
Success by itself = yes
Success with setback = yes, but
Failure with advantage = no, but
Failure by itself = no
Failure with setback = no, and
Success and failure cancel each other out on a 1-for-1 basis, as do advantage and setback, with what remains being your result. Eg. Rolling 4 successes, 2 failures, 2 advantage and 5 setback would give you a result of 2 successes with 3 setback.
Advantage and setback should ideally be used for narrative effects that benefit/hinder the characters. Players are encouraged to contribute ideas, not just the GM, though the GM does have final say. However, the game provides a series of mechanical options should the creative juices not be flowing (or even just the group's preference). Eg. 1 advantage could be used to give the next player a boost die, or the next enemy a setback die; while 3 setback could result in a weapon expending it's ammo pack.
One other pair of results is possible on certain die: Triumph and Despair. These are kind of like "super success" and "super failure": they act as a single success/failure that can cancel out as normal, but they also have a narrative component that cannot be cancelled (generally equivalent to 3 advantage/setback) as a sort of Force ex machina.
Speaking of the Force: Destiny points are a pool of metacurrency that are determined by rolling at the start of a session. They consist of a light side and dark side. Light side are spent by the players, then flipped to dark side. Dark side are spent by the GM and similarly flipped. They're used for the standard metacurrency things.
Characters have familiar "trad" elements of D&D-style attributes (called "characteristics" here) and skills, but the values determine how many dice make up your pool, similar to World of Darkness games. What's different is that the classes are made up of a talent tree, with a choice of starting talents, and subsequent talents requiring a connected one be purchased to be eligible for acquisition. Talents differ in XP cost, and the branching paths differ between classes.
There is an extensive amount of gear on par with games like Cyberpunk and Shadowrun, and a system for modifying it for those players that like mechanical optimisation.
If you do decide to give it go, I highly recommend
Oggdude's Character Generator.
