So I just did a quick test with a few different SNES and GBA emulators.
SNES
blargSNES v1.3
ActRaiser 2 - Doesn't work
Aladdin - Runs perfect
Axelay - Runs perfect
Donkey Kong Country - Runs perfect
Retroarch PocketSNES v7.2.0 (1.3.6)
ActRaiser 2 - Runs perfect
Aladdin - Runs perfect
Axelay - Runs perfect but noticed some screen tearing on the left hand side
Donkey Kong Country - Runs perfect but noticed some screen tearing on the left hand side
Retroarch SNES9x Next v1.52.4 (1.3.6)
ActRaiser 2 - Runs slow
Aladdin - Runs slow
Axelay - Runs slow
Donkey Kong Country - Runs slow
GBA
mGBA nightly build
Aladdin - Runs a little slow
Donkey Kong Country - Runs a little slow
Drill Dozer - Runs a little slow
Retroarch mGBA git (1.3.6)
Aladdin - Runs slow
Donkey Kong Country - Runs slow
Drill Dozer - locks up
Retroarch gpSP v0.91 (1.3.6)
Aladdin - Runs great. A little screen tearing
Donkey Kong Country - Runs perfectly
Drill Dozer - Locks up
Now i know there are a lot of settings that can be adjusted with the Retroarch emus, so very likely you could get better results with them (I am using default settings).
So in my opinion I would stick with blargSNES or PocketSNES for SNES stuff and gpSP for GBA stuff.