The emulator I use is the newest version of Visual Boy advance.
I use DirectSound with the Primary Sound driver.
The emulator gives the option to specify the "Number of sound buffers:" which I set to
"5 frames = 83.33 ms".
I also tried switching to DirectX's XAudio2 which according to this
http://www.gamefaqs.com/boards/914622-mother-3/55586804 internet post sort of reduces the latency, and it does, the downside is that the audio is noticeably worse (part of what makes the game great is the awesome music, I daresay the music is part of the story itself).
Another factor is the keyboard input latency, which might be faster on the GBA. In any case, when I press the corresponding A or B key on my keyboard, the button sound (when you navigate in-game menus itll make sounds) sounds undoubtedly dissonant to the keystroke. I play piano, and the latency of keystroke to piano-sound is much lower.
When I play a midi-keyboard on my computer using the primary sound driver, the latency really throws me off and I can hardly play, but when I use a special driver called ASIO-4-ALL it works much better.
Lastly I would like to add that this problem is something many people have, especially if the sound card, sound driver etc. isn't the best. It all depends on the hardware and its driver.
edit: and thanks FAST6191 for the emulator tip, I'll try it out sometime tonight (German night). If you can hack the rom I'd be delighted.