Honestly, while I am a major fan of the Amiga, I'd say that the AT was the better machine, as it had eight ISA slots, which meant far more expansion opportunity. Then again, each machine had its own niche: The ST was great for music with its built-in MIDI ports, the Amiga was awesome for video editing due to its genlock capabilities, the Macintosh had a lot of good desktop publishing tools, and the AT was a good well-rounded machine with all of its expansion opportunities.
As an off the shelf product the Amiga could not be beaten. It was only through expansion that the PC could compete, adding sound/graphics cards. When price came into it though both the ST and Amiga were far cheaper than the PC.
For desktop publishing and musicians the Atari ST was the better value. For multitasking, gaming and everything else, the Amiga was the better system. The AT was too bulky, too expensive, albeit a lot of professional programs were available for it (WordPerfect, Lotus 1-2-3, dBase, Turbo Pascal, etc…) which is why it was popular in the business world.