While I don't think this game does it as well as other works of fiction, I also don't feel like it's handled particularly poorly either.

I remember reading that people from Old Archades are free to pursue employment in the city proper, but end up overwhelmed due to the competitive, demanding nature of Archadian business. I might be reading too deep into that, but I thought that might've been a commentary on Archadia's neglect of the old town and failing to instill an education system to give the impoverished the necessary skills to succeed. Again, that could just be me imprinting my own views on society and government onto the game's writing, but I think there are little incidental details here and there (and really that's the biggest strength FFXII's writing has in lieu of a strong central narrative) that contribute to a subtly nuanced understanding. I like that the game forces you to talk to NPCs from both districts to show the class divide. The subquest in Old Archedes is a bit tonally off-putting, but I still think there's a decent bit of subtext there. I'm personally fine with that, I don't necessarily want every depiction of the poor and homeless to be Les Mis.

In contrast, I think an example of this trope handled poorly lies in FFVI. Zozo, where all of Jidoor's poor and impoverished flocked to [somehow] build their own strikingly modern town (with skyscrapers and everythang). It's a town comprised of liars, cheats, and thieves. At least Old Archades became that way explicitly due to governmental neglect, and there's an attempt to make some NPCs empathetic that is simply not present in Zozo.

As Wolf Kanno said, it's a topic arguably done best in Final Fantasy Tactics; I wish the game kept its focus on the War of the Lions and it's effect on the common people rather than its eventual trajectory, but I guess that's what Tactics Ogre is for? I don't know, I've never actually played it, but it's on the list.