This is what I remember from those times: if you had external gear (synth, sampler etc.) then the Atari was your best bet because of the built-in MIDI ports[1] and consequently having a good ecosystem in terms of MIDI sequencers. (Cubase, for example, was available for ST)[2].
If you didn't have external gear, then you would go for Amiga (maybe using a cheap Amiga sampler interface[3], and a music tracker[4] as the software) due to the fact that Amiga had better onboard audio, courtesy of Paula[5]. (IIRC, it wasn't until the Falcon that Atari caught up with Amiga in terms of onboard audio).
If you didn't have external gear, then you would go for Amiga (maybe using a cheap Amiga sampler interface[3], and a music tracker[4] as the software) due to the fact that Amiga had better onboard audio, courtesy of Paula[5]. (IIRC, it wasn't until the Falcon that Atari caught up with Amiga in terms of onboard audio).
[1] https://info-coach.fr/atari/hardware/interfaces.php
[2] https://www.exxoshost.co.uk/atari/mirror/tamw/cubase.htm
[3] https://www.youtube.com/watch?v=i9MXYZh1jcs
[4] https://en.wikipedia.org/wiki/Music_tracker
[5] http://theamigamuseum.com/the-hardware/the-ocs-chipset/paula...