There was some talk before about the Falcon being the preferred music tool of the time. A quick look at the specs confirms this:
Falcon: 16-bit with 8 stereo channels.
Amiga1200: 8-bit with 4 stereo channels.
I don't know much about Atari's though. I'm just looking at the specs. I think Bloodline might know.
*EDIT: shhit he already posted.
The Falcon was a better machine for 1993, but I took the OP's question as looking at the machines now.
Back in the day, the Atari had better MIDI support and consequently more mature software. The Falcon just added good quality Audio to that.
Now, the cheapest PC/Mac will have better quality Audio, better software (for free), and better support for modern instruments (which tend to use USB over MIDI ports) than any Atari.
The Amiga on the other hand, can have a cheap MIDI box added, has some interesting software (some find these strange packages very creative, myself included) and still as a unique audio sound that can't be reproduced easily on modern hardware.
And yes. I will always throw my tuppence in a music thread

-edit- for the record I do actually have an Atari ST here, but I'm only keeping it around so I can see AROS run on it one day

hahaha