After reading your comment I had to check out the situation in the case of Donkey Kong Country, since that series has some of the most impressive SNES soundtracks in my opinion.
While they did an impressive job, there is still a distinct difference between the two systems.
GBA: https://youtu.be/UlTgFb0qbxQ
SNES: https://youtu.be/_4EjGXRDOH0
edit: They added some interesting didgeridoo-like sound effects to "Forest Frenzy" though