Graphics abilities: The Amiga had 4,096 colors as opposed to the ST’s 512, and had a blitter chip that the ST lacked. The Atari eventually got both of these abilities with the 520 and 1040 STe, but that did not come until late 1989.
Sound/Music: The Amiga had 4-channel stereo sound, while the ST only had mono. However, Atari once again got this ability with the release of the STe. Seems like they should have released the STe from the start!
Turning the machine on and off, and resetting: The fact that the power switch is on the power brick on the Amiga 500 is horrendous. While the original 520 ST did have a brick as well, at the very least the power switch wasn’t on it. It also had a reset button, something which the A500 also lacked. And by 1987, the power supply was internally inside the ST. Not so with the A500.
Miscellaneous: I like that I can mess around in TOS/GEM with no floppy disk. Sure, you can’t do much, but I can at least test the mouse, keys, and play around a bit. Not so on the A500. The only thing that you can do is without a disk is watch the screen with the guy’s hand holding a floppy. That’s it.
Looks: This one is purely opinion, but the 520/1040 ST/STe is a lot sexier than the A500. It just looks better. Again, this is purely opinion.