The GBA doesn't always have lower quality. I find this especially true for V Advance, I vastly prefer the music there to the SNES OST (especially on 'The Decisive Battle'). Also, the FF I DoS Final Battle track for FF I sounds so much more epic on the GBA compared to the FF Origins or Aniversary editions, IMHO.

I used to listen to FF I and II DoS Music Player a lot. Now, not so much anymore. But I always thought the music player was a nice addition.