Hate to spoil the rivalry and sit on the fence but:
Didn't anyone here have an ST and then UPGRADED to an Amiga?
I bought an ST in 1987, just before they started fitting double sided disk drives in the things. My first three games, on plain black disks that cost a fortune back then (£2 each?), were Super Sprint, Barbarian and Star Wars.
I love these three games - superb playability. The first ever ST game I played was plutos - I thought the graphics were amazing back then but it hasn't aged to well!
In 1989 (I think!) I sold the ST and bought an amiga batman pack after being jealous of a friend. Must admit, I prefer the Amiga but the ST was a good games machine for the 2 years I had it.
Some vector flight sims (eg Falcon) ran better on the ST because of its slightly faster processor. That's about the only thing it had above the Amiga.