Most of the arcade machines use a Yamaha FM chip (like the Megadrive), and thus are restricted to FM sounds. The Amiga can playback samples, thus opening it up to greater variety of timbres. You'll probably find that the arcade stuff is done mostly using MIDI, and a custom FM sound editor. Trackers have much tighter control over playback nuances than the MIDI spec, and make it much easier to make more dynamic-sounding pieces in a low number of channels.
BTW, although I built my career on it, and it sounded better than anything bar the SID at the time, the Paula chip is a bit crap really. 8-bit, four sample channels, and that's it. No filters or anything. Full marks to people like Jochen Hippel and Rhino (TeamHoi) for writing players with generated synth sounds in (not "chip" sounds).