GBA why is this even a meow competition.

It's tough to pick, but I suppose I'll go with DS for a few reasons.
Animal Crossing
Mario Kart DS: Super Circuit is one of the few MK games I've barely played, and the controls and physics are too tough for me.
DSi: It unfortunately removes the GBA port, but adds a camera, more processing power, and DSiWare.
3D games: Yeah, 3D titles are still primitive on DS. But they're clearly more sophisticated than the few barely 3D games on GBA.
On the DS and DS Lite you can play GBA games. A GBA+DS combo is probably a better library than GB+GBC+GBA.

It's tough, though. GBA SP is compact and awesome and of course opens up the GB+GBC libraries. For what it's also worth, no DS games make it on my Top 50 of all-time, but Mother 3 and Super Mario Advance 2 (combined with the SNES version of SMW per the list rules) are in my Top 25.
So basically, the higher highs of GBA software are better, but the DS offers more variety.

I would go with GBA.

The GBA just has more games that I go back to regularly. Kirby and the Amazing Mirror, Metroid Fusion/Zero Mission, Mega Man Zero, Mario and Luigi, Astro Boy, Golden Suns.

The DS doesn't have too many games I replay very often. Kirby Superstar Ultra, Bowser's Inside Story, and the Phoenix Wright games. Nothing else really comes to mind for me.

So GBA for me.

I liked and still like the GBA better because I felt and feel it was more "core". It was basically a SNES emulator in the palm of your hand. The DS was more like the Wii, in that it was trying to be something brand new and different, hence games like Nintendogs and the over-reliance on two screens and a stylus. And while I did own a DS and enjoyed it, that was just not as enjoyable to me as the no-frills, straight-up beast that was the GBA--the last of the Gameboys.

Though I have the give the DS credit for it's backwards compatiability.

Too bad GBA was killed early, I know it still had decent support after DS launched but imagine if it was Nintendo’s only handheld in 2005 & most of 2006 with DS not coming until holiday 2006.

Astoryboy omega factor what a masterpiece, it also had the Mega man Zero quadrology, that was another set of magnificent games, the golden sun duology, fire emblem original games, it gave origin to series like Wario Ware inc, mario and luigi rpgs, it had ports/remakes but also proper continuations of games like metroid fusion, wario land 4.