Boy, are you lucky my friends have been asking me the same specific question over the holidays.
The FF GBA games are actually ports of the PS1 Origins and Anthology collections, but include a number of enhanced features to facilitate a portable console (such as being able to save anywhere you want). And while there are certain limitations compared to the PS1 (GBA version only has 3 save slots) there also a number of extras (beside from both I & II being on the same cart) including extra equipment, streamlined character progression, extra dungeons, extra bosses, and the post game campaign with all the dead characters in FF2. However, at least in the case of FF1, I found the PSP anniversary version to be superior, since it has the excellent Chronodia/Labrynth of Time post game dungeon that takes the entire game to beat.
But if you looking for non-FF RPGs on the GBA, the Golden Sun duology is second to none in terms of gameplay. Memorable music, charming psuedo 3D artstyle, incredible battle system, being able to use spells out of combat to solve puzzles in an immersive way, there's just to much to gush about. The Djinn system alone makes it worth checking out, as once you get enough of them, there's not telling the kinds of crap you can pull off in a fight (especially in the second one). I do gotta say, I think the overarching plot is it's biggest flaw. Having played all the games up to Dark Dawn, I still have no idea what the point of it all was.
Surprisinly, there are acutally not that many traditional turn-based RPGs I can think of on the GBA, most of them being tactical or action rpgs instead.
The original ones would be stuff like Demi Kids: Light/Dark (SMT for babies, not deragotory) Mario & Luigi: Super Star Saga (better than the 3DS remake imo). Mother 3, Riviera: The Promised Land (also has versions on PSP and PC), and Harry Potter: The Prisoner of Azkaban (specifically the 3rd book, as the Chamber of Secrets and Philsophers Stone are action/adventure games). I've never played the Harry Potter one, but I did play the ones on GBC, and those were alright.
There are actually a LOT of remakes and ports for the GBA, including Phantasy Star, Tales of Phantasia, Breath of Fire, Lufia, Lunar, most of which are comprable to their original version.
Action RPGs include stuff like Summon Night, Sword of Mana, Legacy of Goku/Buu's Fury, Tales of the World, and Shining Soul (Shining I & 2 are like Gauntlet, so I recommend using VBA Netplay to team up with friends).
And Strategy or Tactical RPGs? Forget about it! Your swamped for choice with Tactics Ogre, Shining Force (graphically enhanced from the Genesis), Onimusha Tactics, Yggdra Union, Yu-Yu Hakusho: Tournament Tactics (for some reason?), Super Robot Wars (OGs 1 & 2 are natively english, but entries like J, R, A, & D require a translation patch, although A Portable for the PSP is superior) Fire Emblem (because of course). And don't even get me started on Final Fantasy Tactics Advance! That's one of my all time favourite games EVER. But whatever you do, don't get rid of your Black Thread! You get 3 of those in the entire game, and if you lose 1 you won't be able to complete all the missions and unlck the post game stuff!
Megaman: Battle Network 1-6 (but not Battle Chip Challenge), Kingdom Hearts: Chain of Memories, and both Yu-Gi-Oh! The Sacred Cards and Reshef of Destruction are a little harder to categorize. The Yu-Gi-Oh! games are only really fun if you like the card game to begin with, but both Battle Network and Chain of Memories have real time combat with somewhat RPG elements (you're still fucking around with cards a lot though, basically taking the form of your equipment and your abilities).
Castlevania: Circle of the Moon, Harmony of Dissonance and Aria of Sorrow are like Symphony of the Night and have RPG elements, unlike other Metroidvania games on the system like Zero Mission and Fusion.
Don't even ask me what the fuck CIMA: The Enemy is. And if all else fails, you could just lower yourself to playing Pokemon for the umpteenth time.
