The monochrome monitor & mode was way better for productivity than interlaced Amiga high res. MS-DOS compatible floppies. Price. By far.
In any case I don't see them as directly comparable machines. The ST was made to be a cheap Macintosh or PC competitor ("Jackintosh"). Not a multimedia games machine. It wasn't terribly great at games, but it was a great productivity (and MIDI as you say) machine.
Other things the ST was better at:
• single-floppy operation (because the OS was in ROM)
• being useful for productivity with only 1/2MB RAM (ROM again)
• being more affordable until a price war that killed both companies
Me, I owned an Acorn Archimedes. But I used them all.
A single-floppy Mac or Amiga was a massive PITA to use. More RAM helped but didn't cure it. Until adding a hard disk didn't triple the price (end of the 1980s, early 1990s) you needed dual floppies for Mac or Amiga. ST was... OK with one.
However, fundamentally, there were problems that could not be fixed. The entire OS was based on shared memory and message passing based on pointers. Tasks (processes) would read/write each others memory all the time. There was basically no way to implement memory protection without breaking all compatibility.
Why? Because it implemented syscalls through proper TRAPs, for one. While the actual implementation of the core OS wasn't multitasking or even have re-entrant syscalls, others came along and made it so (MiNT, etc) while retaining syscall compatibility. And the thing can be made to use memory protection, etc. even.
The problem with the whole Amiga package is that it was brilliant for 1985, but extremely dated for the mid-90s and the reliance on the custom chips arch there just really couldn't evolve well.
This manifested in 3D games where the processor did all the rasterisation. If the Amiga could bring it's blitter to bare, it won every time. If not, the ST would squeak it.
It's a shame the Blitter chip that came with the STe never shipped with the original ST (wasn't ready in time) and just never really got large market penetration after that. It was actually a decent design.
The STe feature-wise is quite competitive with the Amiga overall, while keeping the simplicity of the ST's architecture. There just wasn't enough of them shipped for software houses to bother making games that used it.
That, and I have a couple Atari Falcon 030s here, and they're really amazing. They really nailed it with that machine, before packing it in.
Better (and very good) video modes, amazing sound, onboard 56k DSP chip & S/PDIF audio, both IDE & SCSI drive support, 68030 processor, up to 14MB RAM.
In the UK, the Atari ST was originally £299 while the Amiga was £499, so it's not really fair to compare the two. I was able to save up for an ST with various weekend and school holiday jobs, but there's no way I could have saved up for an Amiga (and the only classmates I knew with Amigas had their parents buy it for them).
Amiga 500 evened things out a little bit, but it was still a step up.
Price per mhz/MB was better than anything else out there.
Oh, man, that brings back memories. I didn't much get into games, but I did play Sundog on my ST quite a bit.
I remember in the late 80s a neighbor's friend would bring his Korg synth and hook it up to my neighbor's Atari ST. That was quite something.
Another thing the ST had that the Amiga didn't was a port of FTL's Sundog: Frozen Legacy. One of the very best video games of that era. FWIW that little FTL studio then went on to make another incredible hit: Dungeon Master (best selling Atari ST game ever and an incredibly prescient video game).
For whatever reason Dungeon Master got ported to the Amiga but Sundog: Frozen Legacy never did.